{"id":58379,"date":"2020-07-07T11:22:32","date_gmt":"2020-07-07T10:22:32","guid":{"rendered":"https:\/\/groupe-reussite.fr\/?page_id=58379"},"modified":"2025-06-02T12:26:44","modified_gmt":"2025-06-02T11:26:44","slug":"cours-en-ligne-exercices-corriges-theoreme-de-thales","status":"publish","type":"page","link":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-theoreme-de-thales\/","title":{"rendered":"Th\u00e9or\u00e8me de Thales exercices et corrig\u00e9s"},"content":{"rendered":"<div class=\"Latex_page\">\n<section class=\"has_ae_slider elementor-element elementor-section-full_width elementor-reverse-mobile elementor-section-stretched elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default elementor-section elementor-top-section\">\n<div class=\"elementor-container elementor-column-gap-no\">\n<div class=\"elementor-row\">\n<div class=\"elementor-column-wrap elementor-element-populated colone_elementor\">\n<p style=\"text-align: justify;\">\t\t<div data-elementor-type=\"page\" data-elementor-id=\"86176\" class=\"elementor elementor-86176\">\n\t\t\t\t\t\t<div class=\"elementor-inner\">\n\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-top-section elementor-element elementor-element-6f9fb2b3 elementor-section-content-bottom elementor-section-boxed elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"6f9fb2b3\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5032621c sticky_badeau_colone strick_col ae-bg-gallery-type-default\" data-id=\"5032621c\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-column-wrap\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-top-section elementor-element elementor-element-611bd75f elementor-section-boxed elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"611bd75f\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-55718945 strick_col ae-bg-gallery-type-default\" data-id=\"55718945\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5940f45c elementor-widget elementor-widget-heading\" data-id=\"5940f45c\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<p class=\"elementor-heading-title elementor-size-default\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-tage-mage\/\">Cours en ligne Tage Mage <\/a><\/p>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f9bc725 elementor-widget elementor-widget-heading\" data-id=\"f9bc725\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<p class=\"elementor-heading-title elementor-size-default\">Chapitres du sous-test 2 du Tage Mage<\/p>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-56c02cf0 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"56c02cf0\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-fractions\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Fractions<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-390da5ff elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"390da5ff\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-pourcentages\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Pourcentages<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-da8d658 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"da8d658\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-algebre\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Alg\u00e8bre<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-490ac2aa elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"490ac2aa\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-figures-geometriques\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">G\u00e9om\u00e9trie<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3fd40310 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"3fd40310\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-vitesse\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Vitesse<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6edf1c7e elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"6edf1c7e\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Arithm\u00e9tique<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4f2c805 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"4f2c805\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-puissances\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Puissances<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-447b658 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"447b658\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-regle-de-trois\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Proportionnalit\u00e9<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-53863aa elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"53863aa\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-denombrement\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">D\u00e9nombrement<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-11741389 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"11741389\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-probabilites\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Probabilit\u00e9s<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6ace8ace elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"6ace8ace\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-moyenne-arithmetique-moyenne-ponderee\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Moyenne<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-13f1db2f elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"13f1db2f\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-theoreme-de-pythagore\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Th\u00e9or\u00e8me de Pythagore<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-10d04684 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"10d04684\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-theoreme-de-thales\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Th\u00e9or\u00e8me de Thal\u00e8s<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-691a3a8a elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"691a3a8a\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-racines-carrees\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Racines Carr\u00e9es<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2a5f7bd6 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"2a5f7bd6\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/nous-contacter\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">CONTACTEZ-NOUS<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\n<\/div>\n<div class=\"elementor-column-wrap elementor-element-populated colone_latex\">\n<div class=\"style_pag\" style=\"color: #000; font-family: 'Lato', Sans-serif;\">\n<div class=\"elementor-text-editor elementor-clearfix\" style=\"color: #000000; font-family: Lato, sans-serif; text-align: justify;\">\n<h1 class=\"Latex_page_title\">Exercices corrig\u00e9s th\u00e9or\u00e8me de Thales et sa r\u00e9ciproque<\/h1>\n<\/div>\n<p class=\"colone_latex_ancres\" style=\"color: #000000; font-family: Lato, sans-serif; text-align: center;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-theoreme-de-thales\/\">R\u00e9sum\u00e9 de cours<\/a> <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-theoreme-de-thales\/\">Exercices et corrig\u00e9s<\/a><\/p>\n<p class=\"colone_latex_ancres\" style=\"color: #000000; font-family: Lato, sans-serif; text-align: center;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-tage-mage\/\">Cours en ligne du Tage Mage<\/a><\/p>\n<p style=\"text-align: justify;\">Enseign\u00e9 au coll\u00e8ge, le th\u00e9or\u00e8me de Thal\u00e8s est un des th\u00e9or\u00e8mes les plus importants pour le brevet, au m\u00eame titre que le <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-theoreme-de-pythagore\/\">th\u00e9or\u00e8me de Pythagore<\/a>. Ce th\u00e9or\u00e8me est en effet indispensable pour l&rsquo;\u00e9preuve de brevet en fin de 3\u00e8me. Il est \u00e9galement tr\u00e8s utile aux \u00e9l\u00e8ves qui pr\u00e9parent les concours des \u00e9coles de commerce (Acces et Sesame) en terminale ou encore ) ceux qui pr\u00e9parent le Tage Mage ou le Score IAE en licence pour int\u00e9grer les meilleures \u00e9coles de commerce.<\/p>\n<h2 style=\"text-align: justify;\">Exercice 1 : application directe du cours du th\u00e9or\u00e8me de Thal\u00e8s<\/h2>\n<p class=\"p1\" style=\"text-align: justify;\">Dans la <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-figures-geometriques\/\">figure<\/a> suivante, les droites (BM) et (PC) sont s\u00e9cantes en A . On sait que :<\/p>\n<p class=\"p1\" style=\"text-align: justify;\">AB = 7 cm ; AM = 4 cm ; AP = 6 cm ; AC = 8 cm<\/p>\n<p class=\"p1\" style=\"text-align: justify;\">Les droites (BC) et (PM) sont-elles parall\u00e8les ?<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" class=\"size-full wp-image-58411 aligncenter\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2020\/07\/Exercice-thales-rectangle.jpg\" alt=\"exercice 1 theoreme thales\" width=\"400\" height=\"235\" \/><\/p>\n<h2 style=\"text-align: justify;\">Exercice 2 : Une construction appliquant le th\u00e9or\u00e8me de Thal\u00e8s<\/h2>\n<p id=\"E356\" style=\"text-align: justify;\">La figure ci-contre n\u2019est pas en vraie grandeur. On donne les informations suivantes :<\/p>\n<p style=\"text-align: justify;\">\u2022 Le triangle ADE a pour dimensions : AD = 7 cm, AE = 4,2 cm et DE = 5,6 cm.<br \/>\n\u2022 F est le point de [AD] tel que AF = 2,5 cm.<br \/>\n\u2022 B est le point de [AD) et C est le point de [AE) tels que : AB = AC = 9 cm.<br \/>\n\u2022 La droite (FG) est parall\u00e8le \u00e0 la droite (DE).<\/p>\n<p style=\"text-align: justify;\">Calculer la longueur FG.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" class=\"size-full wp-image-58412 aligncenter\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2020\/07\/construction-theoreme-thales.jpg\" alt=\"exercice-construction thales\" width=\"400\" height=\"349\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">\t\t<div data-elementor-type=\"section\" data-elementor-id=\"84983\" class=\"elementor elementor-84983\">\n\t\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-inner-section elementor-element elementor-element-51d9c4d elementor-section-content-bottom full_width elementor-section-full_width elementor-section-height-min-height elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"51d9c4d\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-narrow\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-66 elementor-inner-column elementor-element elementor-element-610eeeb9 ae-bg-gallery-type-default\" data-id=\"610eeeb9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5bf69eb8 elementor-widget elementor-widget-heading\" data-id=\"5bf69eb8\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">COURS DE MATHS<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-49568da4 elementor-widget elementor-widget-heading\" data-id=\"49568da4\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Les meilleurs professeurs particuliers<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1eb9e0cb elementor-widget elementor-widget-heading\" data-id=\"1eb9e0cb\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Pour progresser et r\u00e9ussir<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-15c3e28d elementor-align-left elementor-mobile-align-center elementor-widget elementor-widget-button\" data-id=\"15c3e28d\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/cours-particuliers\/maths\/tous-niveaux\/france\/\" target=\"_blank\" class=\"elementor-button-link elementor-button elementor-size-md\" role=\"button\" id=\"CTA_PRD_CP\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Cours particuliers maths<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1a5c10e7 elementor-widget elementor-widget-text-editor\" data-id=\"1a5c10e7\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p style=\"text-align: left\"><b>Avis Google France <\/b><span style=\"color: #e5a430\"><b>\u2605\u2605\u2605\u2605\u2605<\/b><\/span><b> 4,9 sur 5<\/b><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-6913d4fe ae-bg-gallery-type-default\" data-id=\"6913d4fe\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\n<p>&nbsp;<\/p>\n<h2 style=\"text-align: justify;\">Exercice 3 : Le th\u00e9or\u00e8me de Thal\u00e8s dans une voile<\/h2>\n<p style=\"text-align: justify;\">Un centre nautique souhaite effectuer une r\u00e9paration sur une voile.<\/p>\n<p style=\"text-align: justify;\">La voile a la forme du triangle PMW ci-dessous.<\/p>\n<p style=\"text-align: justify;\">1. On souhaite faire une couture suivant le segment [CT].<br \/>\n1. a. Si (CT) est parall\u00e8le \u00e0 (MW), quelle sera la longueur de cette couture ?<br \/>\n1. b. La quantit\u00e9 de fil n\u00e9cessaire est le double de la longueur de la couture. Est-ce que 7 m\u00e8tres de fil suffiront ?<br \/>\n2. Une fois la couture termin\u00e9e, on mesure : PT = 1,88 m et PW = 2,30 m. La couture est-elle parall\u00e8le \u00e0 (MW ) ?<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" class=\"size-full wp-image-58413 aligncenter\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2020\/07\/triangle-exercice-thales.jpg\" alt=\"application theoreme thales\" width=\"250\" height=\"364\" \/><\/p>\n<h2 style=\"text-align: justify;\">Exercice 4 : Le th\u00e9or\u00e8me de Thales et triangle rectangle<\/h2>\n<p id=\"E370\" style=\"text-align: justify;\"><em>On consid\u00e8re la figure ci-dessous qui n\u2019est pas \u00e0 l\u2019\u00e9chelle.<\/em><\/p>\n<ul style=\"text-align: justify;\">\n<li>Le triangle JAB est rectangle en A.<\/li>\n<li>Les droites (MU) et (AB) sont parall\u00e8les.<\/li>\n<li>Les points A, M et J sont align\u00e9s.<\/li>\n<li>Les points C, U et J sont align\u00e9s.<\/li>\n<li>Les points A, C et B sont align\u00e9s.<\/li>\n<li>AB = 7,5 m.<\/li>\n<li>MU = 3 m.<\/li>\n<li>JM = 10 m.<\/li>\n<li>JB = 19,5 m.<\/li>\n<li>AJ = 18 m<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">Montrer que la longueur AC est \u00e9gale \u00e0 5,4 m.<\/p>\n<h2 style=\"text-align: justify;\"><img loading=\"lazy\" class=\"size-full wp-image-58414 aligncenter\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2020\/07\/triangle-thales.jpg\" alt=\"exercice theoreme thales\" width=\"400\" height=\"421\" \/><\/h2>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;\t\t&lt;div data-elementor-type=&quot;section&quot; data-elementor-id=&quot;41419&quot; class=&quot;elementor elementor-41419&quot;&gt;\n\t\t\t\t\t&lt;div class=&quot;elementor-section-wrap&quot;&gt;\n\t\t\t\t\t\t\t\t&lt;section class=&quot;has_ae_slider elementor-section elementor-inner-section elementor-element elementor-element-2fe5e484 elementor-section-content-bottom full_width elementor-section-full_width elementor-section-height-min-height elementor-section-height-default ae-bg-gallery-type-default&quot; data-id=&quot;2fe5e484&quot; data-element_type=&quot;section&quot; data-settings=&quot;{&quot;background_background&quot;:&quot;classic&quot;}&quot;&gt;\n\t\t\t\t\t\t&lt;div class=&quot;elementor-container elementor-column-gap-narrow&quot;&gt;\n\t\t\t\t\t\t\t&lt;div class=&quot;elementor-row&quot;&gt;\n\t\t\t\t\t&lt;div class=&quot;has_ae_slider elementor-column elementor-col-66 elementor-inner-column elementor-element elementor-element-6795a20c ae-bg-gallery-type-default&quot; data-id=&quot;6795a20c&quot; data-element_type=&quot;column&quot;&gt;\n\t\t\t&lt;div class=&quot;elementor-column-wrap elementor-element-populated&quot;&gt;\n\t\t\t\t\t\t\t&lt;div class=&quot;elementor-widget-wrap&quot;&gt;\n\t\t\t\t\t\t&lt;div class=&quot;elementor-element elementor-element-b2373a6 elementor-widget elementor-widget-heading&quot; data-id=&quot;b2373a6&quot; data-element_type=&quot;widget&quot; data-widget_type=&quot;heading.default&quot;&gt;\n\t\t\t\t&lt;div class=&quot;elementor-widget-container&quot;&gt;\n\t\t\t&lt;h3 class=&quot;elementor-heading-title elementor-size-default&quot;&gt;COURS A DOMICILE&lt;\/h3&gt;\t\t&lt;\/div&gt;\n\t\t\t\t&lt;\/div&gt;\n\t\t\t\t&lt;div class=&quot;elementor-element elementor-element-aa84a8d elementor-widget elementor-widget-heading&quot; data-id=&quot;aa84a8d&quot; data-element_type=&quot;widget&quot; data-widget_type=&quot;heading.default&quot;&gt;\n\t\t\t\t&lt;div class=&quot;elementor-widget-container&quot;&gt;\n\t\t\t&lt;h4 class=&quot;elementor-heading-title elementor-size-default&quot;&gt;Des cours sur mesure de qualit\u00e9&lt;\/h4&gt;\t\t&lt;\/div&gt;\n\t\t\t\t&lt;\/div&gt;\n\t\t\t\t&lt;div class=&quot;elementor-element elementor-element-b64d2eb elementor-widget elementor-widget-heading&quot; data-id=&quot;b64d2eb&quot; data-element_type=&quot;widget&quot; data-widget_type=&quot;heading.default&quot;&gt;\n\t\t\t\t&lt;div class=&quot;elementor-widget-container&quot;&gt;\n\t\t\t&lt;h4 class=&quot;elementor-heading-title elementor-size-default&quot;&gt;POUR ACC\u00c9L\u00c9RER MA PROGRESSION&lt;\/h4&gt;\t\t&lt;\/div&gt;\n\t\t\t\t&lt;\/div&gt;\n\t\t\t\t&lt;div class=&quot;elementor-element elementor-element-23b182ab elementor-align-left elementor-mobile-align-center elementor-widget elementor-widget-button&quot; data-id=&quot;23b182ab&quot; data-element_type=&quot;widget&quot; data-widget_type=&quot;button.default&quot;&gt;\n\t\t\t\t&lt;div class=&quot;elementor-widget-container&quot;&gt;\n\t\t\t\t\t&lt;div class=&quot;elementor-button-wrapper&quot;&gt;\n\t\t\t&lt;a href=&quot;https:\/\/groupe-reussite.fr\/cours-particuliers\/toutes-matieres\/tous-niveaux\/france\/&quot; target=&quot;_blank&quot; class=&quot;elementor-button-link elementor-button elementor-size-md&quot; role=&quot;button&quot; id=&quot;CTA_PRD_CP&quot;&gt;\n\t\t\t\t\t\t&lt;span class=&quot;elementor-button-content-wrapper&quot;&gt;\n\t\t\t\t\t\t&lt;span class=&quot;elementor-button-text&quot;&gt;Professeur particulier \u00e0 domicile&lt;\/span&gt;\n\t\t&lt;\/span&gt;\n\t\t\t\t\t&lt;\/a&gt;\n\t\t&lt;\/div&gt;\n\t\t\t\t&lt;\/div&gt;\n\t\t\t\t&lt;\/div&gt;\n\t\t\t\t&lt;div class=&quot;elementor-element elementor-element-1a65b816 elementor-widget elementor-widget-text-editor&quot; data-id=&quot;1a65b816&quot; data-element_type=&quot;widget&quot; data-widget_type=&quot;text-editor.default&quot;&gt;\n\t\t\t\t&lt;div class=&quot;elementor-widget-container&quot;&gt;\n\t\t\t\t\t\t\t\t&lt;div class=&quot;elementor-text-editor elementor-clearfix&quot;&gt;\n\t\t\t\t&lt;p style=&quot;text-align: left;&quot;&gt;&lt;b&gt;Avis Google France &lt;\/b&gt;&lt;span style=&quot;color: #e5a430;&quot;&gt;&lt;b&gt;\u2605\u2605\u2605\u2605\u2605&lt;\/b&gt;&lt;\/span&gt;&lt;b&gt; 4,9 sur 5&lt;\/b&gt;&lt;\/p&gt;\t\t\t\t\t&lt;\/div&gt;\n\t\t\t\t\t\t&lt;\/div&gt;\n\t\t\t\t&lt;\/div&gt;\n\t\t\t\t\t\t&lt;\/div&gt;\n\t\t\t\t\t&lt;\/div&gt;\n\t\t&lt;\/div&gt;\n\t\t\t\t&lt;div class=&quot;has_ae_slider elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-14d96707 ae-bg-gallery-type-default&quot; data-id=&quot;14d96707&quot; data-element_type=&quot;column&quot;&gt;\n\t\t\t&lt;div class=&quot;elementor-column-wrap&quot;&gt;\n\t\t\t\t\t\t\t&lt;div class=&quot;elementor-widget-wrap&quot;&gt;\n\t\t\t\t\t\t\t\t&lt;\/div&gt;\n\t\t\t\t\t&lt;\/div&gt;\n\t\t&lt;\/div&gt;\n\t\t\t\t\t\t\t\t&lt;\/div&gt;\n\t\t\t\t\t&lt;\/div&gt;\n\t\t&lt;\/section&gt;\n\t\t\t\t\t\t\t&lt;\/div&gt;\n\t\t\t\t&lt;\/div&gt;\n\t\t&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:705,&quot;3&quot;:{&quot;1&quot;:0},&quot;9&quot;:1,&quot;10&quot;:1,&quot;12&quot;:0}\" data-sheets-formula=\"=CONCATENER(&quot;C[-2];&quot;]&quot;)\">\t\t<div data-elementor-type=\"section\" data-elementor-id=\"41419\" class=\"elementor elementor-41419\">\n\t\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-inner-section elementor-element elementor-element-2fe5e484 elementor-section-content-bottom full_width elementor-section-full_width elementor-section-height-min-height elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"2fe5e484\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-narrow\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-66 elementor-inner-column elementor-element elementor-element-6795a20c ae-bg-gallery-type-default\" data-id=\"6795a20c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b2373a6 elementor-widget elementor-widget-heading\" data-id=\"b2373a6\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">COURS A DOMICILE<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-aa84a8d elementor-widget elementor-widget-heading\" data-id=\"aa84a8d\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Des cours sur mesure de qualit\u00e9<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b64d2eb elementor-widget elementor-widget-heading\" data-id=\"b64d2eb\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">POUR ACC\u00c9L\u00c9RER MA PROGRESSION<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-23b182ab elementor-align-left elementor-mobile-align-center elementor-widget elementor-widget-button\" data-id=\"23b182ab\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/cours-particuliers\/toutes-matieres\/tous-niveaux\/france\/\" target=\"_blank\" class=\"elementor-button-link elementor-button elementor-size-md\" role=\"button\" id=\"CTA_PRD_CP\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Professeur particulier \u00e0 domicile<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1a65b816 elementor-widget elementor-widget-text-editor\" data-id=\"1a65b816\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p style=\"text-align: left;\"><b>Avis Google France <\/b><span style=\"color: #e5a430;\"><b>\u2605\u2605\u2605\u2605\u2605<\/b><\/span><b> 4,9 sur 5<\/b><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-14d96707 ae-bg-gallery-type-default\" data-id=\"14d96707\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<\/span><\/p>\n<p>&nbsp;<\/p>\n<h2 style=\"text-align: justify;\">Exercice 5 : La r\u00e9ciproque du th\u00e9or\u00e8me de Thal\u00e8s avec des triangles invers\u00e9s<\/h2>\n<p style=\"text-align: justify;\">On consid\u00e8re la figure ci-contre pour laquelle :<\/p>\n<p style=\"text-align: justify;\">AN = AN\u2019= 2 cm, AM =3 cm, AB = 9 cm et AC = 6 cm.<\/p>\n<p style=\"text-align: justify;\">Les droites (MN) et (BC) sont-elles parall\u00e8les ?<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" class=\"size-full wp-image-58419 aligncenter\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2020\/07\/triangle-inverse-thales.jpg\" alt=\"triangle inverse thales exercice\" width=\"200\" height=\"212\" \/><\/p>\n<h3 style=\"text-align: justify;\"><\/h3>\n<h2 style=\"text-align: justify;\">Exercice 6 : La r\u00e9ciproque du th\u00e9or\u00e8me de Thal\u00e8s sur un triangle<\/h2>\n<p style=\"text-align: justify;\">On a SM = 4, SA = 12, SN = 6 et SB = 18<\/p>\n<p style=\"text-align: justify;\">Les droites (AB) et (MN) sont-elles parall\u00e8les ?<\/p>\n<h3 style=\"text-align: justify;\"><img loading=\"lazy\" class=\"size-full wp-image-58420 aligncenter\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2020\/07\/pyramide-thales-exercice.jpg\" alt=\"triangle exercice theoreme thales\" width=\"242\" height=\"215\" \/><\/h3>\n<h3 style=\"text-align: justify;\"><\/h3>\n<h2 style=\"text-align: justify;\">Exercice 7 : R\u00e9ciproque du th\u00e9or\u00e8me de Thal\u00e8s sur une figure quelconque<\/h2>\n<p style=\"text-align: justify;\">Soit ABC un triangle dans lequel on a trac\u00e9 une droite (ED) parall\u00e8le \u00e0 la droite (BC)<\/p>\n<p style=\"text-align: justify;\">On a AE = BC = 3 et EB = AD = 2<\/p>\n<p style=\"text-align: justify;\">1) Calculer AC, DC et ED<\/p>\n<p style=\"text-align: justify;\">2) F est un point de (DE) tel que DF = 2,7<\/p>\n<p style=\"text-align: justify;\">D\u00e9terminer si les droites (EC) et (AF) sont parall\u00e8les.<\/p>\n<h3 style=\"text-align: justify;\"><img loading=\"lazy\" class=\"size-full wp-image-58421 aligncenter\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2020\/07\/thales-figure-quelquonque.jpg\" alt=\"application thales avec figure quelconque\" width=\"309\" height=\"260\" \/><\/h3>\n<h3 style=\"text-align: justify;\"><\/h3>\n<h2 style=\"text-align: justify;\">Exercice 8 : sur la r\u00e9ciproque du th\u00e9or\u00e8me de Thales<\/h2>\n<p style=\"text-align: justify;\">Sur la figure ci-contre<\/p>\n<p style=\"text-align: justify;\">Les droites (AR) et (CT) sont parall\u00e8les.<\/p>\n<p style=\"text-align: justify;\">Les points E, L, R, T et C, A, L, B sont align\u00e9s dans l\u2019ordre respectif<\/p>\n<p style=\"text-align: justify;\">On a \u00e9galement, LC = 6 ; LT = 9 ; LA = 4,8 ; LB = 1,5 et LE = 3<br \/>\n1) Calculer LR<br \/>\n2) D\u00e9terminer si les droites (EB) et (CT) sont parall\u00e8les<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" class=\"size-full wp-image-58422 aligncenter\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2020\/07\/dernier-exercice-thales.jpg\" alt=\"exercice application thales\" width=\"300\" height=\"201\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">\t\t<div data-elementor-type=\"section\" data-elementor-id=\"184942\" class=\"elementor elementor-184942\">\n\t\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-inner-section elementor-element elementor-element-69679e12 elementor-section-content-bottom full_width elementor-section-full_width elementor-section-height-min-height elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"69679e12\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-46679596 ae-bg-gallery-type-default\" data-id=\"46679596\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-56f21768 elementor-headline--style-highlight elementor-widget elementor-widget-animated-headline\" data-id=\"56f21768\" data-element_type=\"widget\" data-settings=\"{&quot;highlighted_text&quot;:&quot;le brevet ?&quot;,&quot;headline_style&quot;:&quot;highlight&quot;,&quot;marker&quot;:&quot;circle&quot;,&quot;loop&quot;:&quot;yes&quot;,&quot;highlight_animation_duration&quot;:1200,&quot;highlight_iteration_delay&quot;:8000}\" data-widget_type=\"animated-headline.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-headline\">\n\t\t\t\t\t<span class=\"elementor-headline-plain-text elementor-headline-text-wrapper\">Tu veux r\u00e9ussir<\/span>\n\t\t\t\t<span class=\"elementor-headline-dynamic-wrapper elementor-headline-text-wrapper\">\n\t\t\t\t\t<span class=\"elementor-headline-dynamic-text elementor-headline-text-active\">le brevet ?<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<\/h3>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-947b9ba elementor-position-left elementor-vertical-align-middle elementor-view-default elementor-mobile-position-top elementor-widget elementor-widget-icon-box\" data-id=\"947b9ba\" data-element_type=\"widget\" data-widget_type=\"icon-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-icon-box-wrapper\">\n\t\t\t\t\t\t<div class=\"elementor-icon-box-icon\">\n\t\t\t\t<span class=\"elementor-icon elementor-animation-\" >\n\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-check-square\"><\/i>\t\t\t\t<\/span>\n\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"elementor-icon-box-content\">\n\t\t\t\t<h4 class=\"elementor-icon-box-title\">\n\t\t\t\t\t<span  >\n\t\t\t\t\t\tProfite des meilleurs exercices et annales\t\t\t\t\t<\/span>\n\t\t\t\t<\/h4>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4b4e6b27 elementor-position-left elementor-vertical-align-middle elementor-view-default elementor-mobile-position-top elementor-widget elementor-widget-icon-box\" data-id=\"4b4e6b27\" data-element_type=\"widget\" data-widget_type=\"icon-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-icon-box-wrapper\">\n\t\t\t\t\t\t<div class=\"elementor-icon-box-icon\">\n\t\t\t\t<span class=\"elementor-icon elementor-animation-\" >\n\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-square\"><\/i>\t\t\t\t<\/span>\n\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"elementor-icon-box-content\">\n\t\t\t\t<h4 class=\"elementor-icon-box-title\">\n\t\t\t\t\t<span  >\n\t\t\t\t\t\tLes meilleurs professeurs t'aideront individuellement\t\t\t\t\t<\/span>\n\t\t\t\t<\/h4>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5e559f50 elementor-position-left elementor-vertical-align-middle elementor-view-default elementor-mobile-position-top elementor-widget elementor-widget-icon-box\" data-id=\"5e559f50\" data-element_type=\"widget\" data-widget_type=\"icon-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-icon-box-wrapper\">\n\t\t\t\t\t\t<div class=\"elementor-icon-box-icon\">\n\t\t\t\t<span class=\"elementor-icon elementor-animation-\" >\n\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-square\"><\/i>\t\t\t\t<\/span>\n\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"elementor-icon-box-content\">\n\t\t\t\t<h4 class=\"elementor-icon-box-title\">\n\t\t\t\t\t<span  >\n\t\t\t\t\t\tPr\u00e9pare le lyc\u00e9e en maths, physique-chimie et fran\u00e7ais\t\t\t\t\t<\/span>\n\t\t\t\t<\/h4>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-60fb8f61 elementor-widget elementor-widget-text-editor\" data-id=\"60fb8f61\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"color: #163153;\">99% de satisfaction lors de nos stages de pr\u00e9paration en 3eme au brevet<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-385c5b2e ae-bg-gallery-type-default\" data-id=\"385c5b2e\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-418c6e6f elementor-align-center elementor-widget elementor-widget-button\" data-id=\"418c6e6f\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/stages\/toutes-matieres\/3eme\/france\/toutes-periodes\/\" target=\"_blank\" class=\"elementor-button-link elementor-button elementor-size-lg\" role=\"button\" id=\"CTA_PRD_STAGE\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Stage de pr\u00e9paration au brevet<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a566ca0 elementor-widget elementor-widget-text-editor\" data-id=\"a566ca0\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p style=\"text-align: center;\"><b>Avis Google France <br \/><\/b><span style=\"color: #e5a430;\"><b>\u2605\u2605\u2605\u2605\u2605<\/b><\/span><b> 4,9 sur 5<\/b><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\n<h2 class=\"p1\" style=\"text-align: justify;\"><\/h2>\n<h2 style=\"text-align: justify;\">Corrig\u00e9 de l&rsquo;exercice 1 : application du th\u00e9or\u00e8me de Thales<\/h2>\n<p style=\"text-align: justify;\">Dans la figure suivante, les droites (BM) et (PC) sont s\u00e9cantes en A .<\/p>\n<p style=\"text-align: justify;\">On sait que : B = 7 cm ; AM = 4 cm ; AP = 6 cm ; AC = 8 cm. Les droites (BC) et (PM) sont-elles parall\u00e8les<\/p>\n<p style=\"text-align: justify;\">Donn\u00e9es : Les points B, A, M et P, A, C sont align\u00e9s dans cet ordre sur deux droites s\u00e9cantes en A.<\/p>\n<p style=\"text-align: justify;\">D\u2019une part : <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-a0498e465fc39c45e1388bb9eeeb0302_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#65;&#77;&#125;&#123;&#65;&#66;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"33\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-ea9b382ea48240c44b349d89d337011d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#52;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-500fb30510e0621a4b2379362c5eef14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#49;&#54;&#125;&#123;&#50;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"18\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\">D\u2019autre part : <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-c94da98ede73a26a0a4fec6342c3fc2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#65;&#80;&#125;&#123;&#65;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"28\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-6d2b69c7e650864477c9914bffcf9a8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#54;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-88c4bfafbe671f6c6f9286457e82fa15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"9\" style=\"vertical-align: -13px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-9c087bd44d9c9c37b648ddf4e48c3864_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#50;&#49;&#125;&#123;&#50;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"18\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\">Conclusion : On n\u2019a donc pas \u00e9galit\u00e9, <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-a0498e465fc39c45e1388bb9eeeb0302_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#65;&#77;&#125;&#123;&#65;&#66;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"33\" style=\"vertical-align: -12px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-1c091d997e66f936737df1f0284817a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#101;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"13\" style=\"vertical-align: -4px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-c94da98ede73a26a0a4fec6342c3fc2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#65;&#80;&#125;&#123;&#65;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"28\" style=\"vertical-align: -12px;\"\/>. De ce fait, d\u2019apr\u00e8s la contrapos\u00e9e du th\u00e9or\u00e8me de Thal\u00e8s, Les droites (BC) et (MP) ne sont pas parall\u00e8les.<\/p>\n<p>Si vous avez des difficult\u00e9s \u00e0 comprendre cette correction ou \u00e0 bien maitriser le th\u00e9or\u00e8me de Thales en 4\u00e8me et 3\u00e8me, n&rsquo;h\u00e9sitez pas \u00e0 faire appel \u00e0 un <a href=\"https:\/\/groupe-reussite.fr\/cours-particuliers\/maths\/tous-niveaux\/france\/\">prof particulier de maths<\/a> pour vous aider \u00e0 pratiquer et comprendre le cours.<\/p>\n<h2 style=\"text-align: justify;\">Corrig\u00e9 de l&rsquo;exercice 2 : construction avec le th\u00e9or\u00e8me de Thales<\/h2>\n<p style=\"text-align: justify;\">Donn\u00e9es : Les points A, F, D et A, G et E sont align\u00e9s sur deux droites s\u00e9cantes en A. Les droites (FG) et (DE) sont parall\u00e8les<\/p>\n<p style=\"text-align: justify;\">Donc d\u2019apr\u00e8s le <em>th\u00e9or\u00e8me de Thal\u00e8s<\/em> on a : <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-1f2ad77b2535f9dae9ec1aa528d5787e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#65;&#70;&#125;&#123;&#65;&#68;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"29\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-45edc77c476d6f72a9bad299da3f9873_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#65;&#71;&#125;&#123;&#65;&#69;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"28\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f57c9dcf5946214179fd279ea79dbec6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#70;&#71;&#125;&#123;&#68;&#69;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"30\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\">Puis en rempla\u00e7ant par les valeurs <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f332a9938ceb86c9bfe7f0f313431a8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#50;&#44;&#53;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"26\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-43391432a02b57453464046bfdd993c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#65;&#71;&#125;&#123;&#52;&#44;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"28\" style=\"vertical-align: -16px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-7af8cef0f61ea5fb3d7e36a0c8cc56fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#70;&#71;&#125;&#123;&#53;&#44;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"28\" style=\"vertical-align: -16px;\"\/><\/p>\n<p style=\"text-align: justify;\">Calcul de FG : On a donc <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f332a9938ceb86c9bfe7f0f313431a8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#50;&#44;&#53;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"26\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-7af8cef0f61ea5fb3d7e36a0c8cc56fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#70;&#71;&#125;&#123;&#53;&#44;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"28\" style=\"vertical-align: -16px;\"\/><\/p>\n<p style=\"text-align: justify;\">Puis FG = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-e480db51b630e8642fe4abd45cf23d16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#50;&#44;&#53;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#53;&#44;&#54;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"73\" style=\"vertical-align: -12px;\"\/> = 2 cm<\/p>\n<h2 style=\"text-align: justify;\">Corrig\u00e9 de l&rsquo;exercice 3 : th\u00e9or\u00e8me de Thal\u00e8s dans une voile<\/h2>\n<p style=\"text-align: justify;\">On souhaite faire une couture suivant le segment [CT].<\/p>\n<p style=\"text-align: justify;\">1. a. Si (CT) est parall\u00e8le \u00e0 (MW), quelle sera la longueur de cette couture ?<\/p>\n<p style=\"text-align: justify;\">Les points P, C, M et P, T, W sont align\u00e9s, et les droites (CT) et (MW) sont parall\u00e8les, on peut donc appliquer le th\u00e9or\u00e8me de Thal\u00e8s,<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-122788f7735edb23045993ecd2745698_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#80;&#67;&#125;&#123;&#80;&#77;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"33\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-52b92a7f8bd9195441dc3f059d0c387c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#67;&#84;&#125;&#123;&#77;&#87;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"39\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\">ou en rempla\u00e7ant par les valeurs connues :<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-89268a244a69c19bda6df26fb4e1827c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#51;&#44;&#55;&#56;&#125;&#123;&#52;&#44;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"35\" style=\"vertical-align: -16px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-007d3507c77850abc1cdc7b90397320e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#67;&#84;&#125;&#123;&#51;&#44;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"27\" style=\"vertical-align: -16px;\"\/><\/p>\n<p style=\"text-align: justify;\">d\u2019o\u00f9 :<\/p>\n<p style=\"text-align: justify;\">CT = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-c24c4a371ba92f4d64a5364005152c4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#51;&#44;&#55;&#56;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#51;&#44;&#52;&#125;&#123;&#52;&#44;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"82\" style=\"vertical-align: -16px;\"\/> = 3,06 m<\/p>\n<p style=\"text-align: justify;\">1. b. La quantit\u00e9 de fil n\u00e9cessaire est le double de la longueur de la couture. Est-ce que 7 m\u00e8tres de fil suffiront?<\/p>\n<p style=\"text-align: justify;\">3,06\u00d72 = 6,12 &lt; 7. Donc 7 m de fil suffiront.<\/p>\n<p style=\"text-align: justify;\">2. Une fois la couture termin\u00e9e, on mesure : P T = 1,88 m et PW = 2,30 m. La couture est-elle parall\u00e8le \u00e0 (MW)?<\/p>\n<p style=\"text-align: justify;\">Donn\u00e9es : Les points P, C, M et P, T, W sont align\u00e9s dans cet ordre sur deux droites s\u00e9cantes en P.<\/p>\n<p style=\"text-align: justify;\">D\u2019une part : <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-122788f7735edb23045993ecd2745698_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#80;&#67;&#125;&#123;&#80;&#77;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"33\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-89268a244a69c19bda6df26fb4e1827c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#51;&#44;&#55;&#56;&#125;&#123;&#52;&#44;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"35\" style=\"vertical-align: -16px;\"\/> = 0,9<\/p>\n<p style=\"text-align: justify;\">D\u2019autre part part : <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-279a9d6c5d46ec4cc2d8d83f7dc6f750_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#80;&#84;&#125;&#123;&#80;&#87;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"34\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-8f0303e8ead4bf0f25ad45405796cfaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#49;&#44;&#56;&#56;&#125;&#123;&#50;&#44;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"35\" style=\"vertical-align: -16px;\"\/> \u2248 0,8<\/p>\n<p style=\"text-align: justify;\">Conclusion : On n\u2019a donc pas \u00e9galit\u00e9, <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-29d99edfdc755575af308c3ff09f65df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#80;&#67;&#125;&#123;&#80;&#77;&#125;&#32;&#92;&#110;&#101;&#113;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#80;&#84;&#125;&#123;&#80;&#87;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"94\" style=\"vertical-align: -12px;\"\/>.<\/p>\n<p style=\"text-align: justify;\">De ce fait, d\u2019apr\u00e8s la contrapos\u00e9e du th\u00e9or\u00e8me de Thal\u00e8s, Les droites (CT) et (MW) ne sont pas parall\u00e8les.<\/p>\n<p style=\"text-align: justify;\">La couture n\u2019a pas \u00e9t\u00e9 faite parall\u00e8le au bord [MW] de la voile.<\/p>\n<h2 style=\"text-align: justify;\">Corrig\u00e9 de l&rsquo;exercice 4 : th\u00e9or\u00e8me de Thal\u00e8s appliqu\u00e9 \u00e0 un triangle<\/h2>\n<p style=\"text-align: justify;\">Montrer que la longueur AC est \u00e9gale \u00e0 5,4 m.<\/p>\n<p style=\"text-align: justify;\">Dans le triangle JAC, les droites (MU) et (AC) sont parall\u00e8les, J, M et A sont align\u00e9s dans cet ordre, J, U et C sont align\u00e9s dans cet ordre : on peut donc appliquer le th\u00e9or\u00e8me de Thal\u00e8s :<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-1ad0a81419102e8d151280538f6907a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#74;&#77;&#125;&#123;&#74;&#65;&#125;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#74;&#85;&#125;&#123;&#74;&#67;&#125;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#77;&#85;&#125;&#123;&#65;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"145\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\">En particulier : <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-50a92c06d921de6d6c5f8ae4b4377e11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#74;&#77;&#125;&#123;&#74;&#65;&#125;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#77;&#85;&#125;&#123;&#65;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"92\" style=\"vertical-align: -12px;\"\/> donc <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-dc09e25c6f9ec76571074717938c339f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#49;&#48;&#125;&#123;&#49;&#56;&#125;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#51;&#125;&#123;&#65;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"73\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\">AC = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f4a05cd3b29be6f132ab337bae72730d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#51;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#49;&#56;&#125;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"49\" style=\"vertical-align: -12px;\"\/> = 5,4 cm<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">\t\t<div data-elementor-type=\"section\" data-elementor-id=\"43481\" class=\"elementor elementor-43481\">\n\t\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-inner-section elementor-element elementor-element-7db513e3 elementor-section-content-bottom full_width elementor-section-full_width elementor-section-height-min-height elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"7db513e3\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-narrow\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-66 elementor-inner-column elementor-element elementor-element-36c4fe19 ae-bg-gallery-type-default\" data-id=\"36c4fe19\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-188adf90 elementor-headline--style-highlight elementor-widget elementor-widget-animated-headline\" data-id=\"188adf90\" data-element_type=\"widget\" data-settings=\"{&quot;highlighted_text&quot;:&quot;soutien scolaire ?&quot;,&quot;headline_style&quot;:&quot;highlight&quot;,&quot;marker&quot;:&quot;circle&quot;,&quot;loop&quot;:&quot;yes&quot;,&quot;highlight_animation_duration&quot;:1200,&quot;highlight_iteration_delay&quot;:8000}\" data-widget_type=\"animated-headline.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-headline\">\n\t\t\t\t\t<span class=\"elementor-headline-plain-text elementor-headline-text-wrapper\">Tu as besoin d'un<\/span>\n\t\t\t\t<span class=\"elementor-headline-dynamic-wrapper elementor-headline-text-wrapper\">\n\t\t\t\t\t<span class=\"elementor-headline-dynamic-text elementor-headline-text-active\">soutien scolaire ?<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<\/h3>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1b12c40d elementor-position-left elementor-vertical-align-middle elementor-view-default elementor-mobile-position-top elementor-widget elementor-widget-icon-box\" data-id=\"1b12c40d\" data-element_type=\"widget\" data-widget_type=\"icon-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-icon-box-wrapper\">\n\t\t\t\t\t\t<div class=\"elementor-icon-box-icon\">\n\t\t\t\t<span class=\"elementor-icon elementor-animation-\" >\n\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-check-square\"><\/i>\t\t\t\t<\/span>\n\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"elementor-icon-box-content\">\n\t\t\t\t<h4 class=\"elementor-icon-box-title\">\n\t\t\t\t\t<span  >\n\t\t\t\t\t\tJe r\u00e9vise en autonomie\t\t\t\t\t<\/span>\n\t\t\t\t<\/h4>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e2c37ec elementor-position-left elementor-vertical-align-middle elementor-view-default elementor-mobile-position-top elementor-widget elementor-widget-icon-box\" data-id=\"e2c37ec\" data-element_type=\"widget\" data-widget_type=\"icon-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-icon-box-wrapper\">\n\t\t\t\t\t\t<div class=\"elementor-icon-box-icon\">\n\t\t\t\t<span class=\"elementor-icon elementor-animation-\" >\n\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-check-square\"><\/i>\t\t\t\t<\/span>\n\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"elementor-icon-box-content\">\n\t\t\t\t<h4 class=\"elementor-icon-box-title\">\n\t\t\t\t\t<span  >\n\t\t\t\t\t\tJe progresse avec un prof \u00e0 domicile\t\t\t\t\t<\/span>\n\t\t\t\t<\/h4>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5e44c831 elementor-position-left elementor-vertical-align-middle elementor-view-default elementor-mobile-position-top elementor-widget elementor-widget-icon-box\" data-id=\"5e44c831\" data-element_type=\"widget\" data-widget_type=\"icon-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-icon-box-wrapper\">\n\t\t\t\t\t\t<div class=\"elementor-icon-box-icon\">\n\t\t\t\t<span class=\"elementor-icon elementor-animation-\" >\n\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-check-square\"><\/i>\t\t\t\t<\/span>\n\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"elementor-icon-box-content\">\n\t\t\t\t<h4 class=\"elementor-icon-box-title\">\n\t\t\t\t\t<span  >\n\t\t\t\t\t\tJe m\u2019entra\u00eene durant les vacances en petit groupe\t\t\t\t\t<\/span>\n\t\t\t\t<\/h4>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-2e1addd4 ae-bg-gallery-type-default\" data-id=\"2e1addd4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-59dc97b6 elementor-align-center elementor-widget elementor-widget-button\" data-id=\"59dc97b6\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/soutien-scolaire\/toutes-matieres\/tous-niveaux\/france\/\" target=\"_blank\" class=\"elementor-button-link elementor-button elementor-size-md\" role=\"button\" id=\"CTA_PRD\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Je d\u00e9couvre le soutien scolaire<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7a117965 elementor-widget elementor-widget-text-editor\" data-id=\"7a117965\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p style=\"text-align: center;\"><b>Avis Google France<br \/><\/b><span style=\"color: #e5a430;\"><b>\u2605\u2605\u2605\u2605\u2605<\/b><\/span><b> 4,9 sur 5<\/b><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\n<h2 style=\"text-align: justify;\"><\/h2>\n<h2 style=\"text-align: justify;\">Corrig\u00e9 de l&rsquo;exercice 5 : avec des triangles invers\u00e9s<\/h2>\n<p style=\"text-align: justify;\">On sait que les droites (MB) et (NC) sont s\u00e9cantes en A. On peut alors calculer diff\u00e9rents rapports<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-e88eb214f3b927972e8d0ae8ca65a2bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#65;&#77;&#125;&#123;&#65;&#66;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"33\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-7ef5b30ec587d9cea5bc3b58b144a769_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2e1435fbb34dc827f8ae4d908bf2364d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\">Et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-96b619048a41f8712558311434148d94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#65;&#78;&#125;&#123;&#65;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"30\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b9babde35ff2506fd73ec9f6522107d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2e1435fbb34dc827f8ae4d908bf2364d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\">On en d\u00e9duit que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-e88eb214f3b927972e8d0ae8ca65a2bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#65;&#77;&#125;&#123;&#65;&#66;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"33\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-96b619048a41f8712558311434148d94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#65;&#78;&#125;&#123;&#65;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"30\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2e1435fbb34dc827f8ae4d908bf2364d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\">On sait \u00e9galement que les points M, A, B et N, A, C sont align\u00e9s dans l\u2019ordre respectif<\/p>\n<p style=\"text-align: justify;\">D\u2019apr\u00e8s la r\u00e9ciproque du th\u00e9or\u00e8me de Thal\u00e8s, (MN) et (BC) sont parall\u00e8les.<\/p>\n<h2 style=\"text-align: justify;\">Corrig\u00e9 de l&rsquo;exercice 6 : r\u00e9ciproque du th\u00e9or\u00e8me de Thal\u00e8s sur un triangle<\/h2>\n<p style=\"text-align: justify;\">On compare les diff\u00e9rents rapports dans le triangle,<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-9e7eb56edc51efe5cb9624cd1680f409_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#83;&#77;&#125;&#123;&#83;&#65;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"32\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-c5d8bb21a40ee36e043dbe912f1080c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"18\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2e1435fbb34dc827f8ae4d908bf2364d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-271d48fc91060108d46e8028561837f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#83;&#78;&#125;&#123;&#83;&#66;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"29\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-40c6e1af1afc8a5a28d04d07a343007c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#49;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"18\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2e1435fbb34dc827f8ae4d908bf2364d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\">On en d\u00e9duit que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-9e7eb56edc51efe5cb9624cd1680f409_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#83;&#77;&#125;&#123;&#83;&#65;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"32\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-271d48fc91060108d46e8028561837f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#83;&#78;&#125;&#123;&#83;&#66;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"29\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\">Dans le triangle ABS on a les points S, M, et A align\u00e9s dans le m\u00eame ordre que les points S, N, et B<\/p>\n<p style=\"text-align: justify;\">D\u2019apr\u00e8s la r\u00e9ciproque du th\u00e9or\u00e8me de Thal\u00e8s, (MN) et (AB) sont parall\u00e8les.<\/p>\n<h2 style=\"text-align: justify;\">Corrig\u00e9 de l&rsquo;exercice 7 : r\u00e9ciproque du th\u00e9or\u00e8me de Thal\u00e8s sur une figure quelconque<\/h2>\n<p style=\"text-align: justify;\">1) Les points A, E et B sont align\u00e9s ainsi que les points A, D, et C. D\u2019apr\u00e8s le th\u00e9or\u00e8me de Thal\u00e8s<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-99e03ed2dd1d0a536956fef9324732dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#65;&#69;&#125;&#123;&#65;&#66;&#125;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#65;&#68;&#125;&#123;&#65;&#67;&#125;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#68;&#69;&#125;&#123;&#66;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"141\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\">Donc <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-df868d8f7394bc0b976c75a9dd165f2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#51;&#125;&#123;&#53;&#125;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#50;&#125;&#123;&#65;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"64\" style=\"vertical-align: -12px;\"\/> d\u2019o\u00f9 AC = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2a16f9eb87e5c213b90442ab8558a2db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#49;&#48;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"18\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\">Le point D appartenant \u00e0 [AC] donc DC = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-89902055ac5770e7b40ffe47e44b95d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#49;&#48;&#125;&#123;&#51;&#125;&#32;&#45;&#32;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"49\" style=\"vertical-align: -12px;\"\/> donc <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-1ce74e8d48136d1cc1e5391ea30379d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#68;&#67;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#52;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"64\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-51818bf9896ac525f1a9cc97812ea77e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#51;&#125;&#123;&#53;&#125;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#68;&#69;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"66\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\">Donc <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-85537d697786375610f29b794960b7a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#68;&#69;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#57;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"64\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\">2) On compare les diff\u00e9rents rapports dans le triangle,<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d2bd57e15d594f1dc9b61c8d0e735077_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#68;&#70;&#125;&#123;&#68;&#69;&#125;&#32;&#61;&#32;&#50;&#44;&#55;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#53;&#125;&#123;&#57;&#125;&#32;&#61;&#32;&#49;&#44;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"163\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-41c3d55298774a82418deed2f73d5889_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#68;&#65;&#125;&#123;&#68;&#67;&#125;&#32;&#61;&#32;&#50;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#51;&#125;&#123;&#52;&#125;&#32;&#61;&#32;&#49;&#44;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"146\" style=\"vertical-align: -12px;\"\/> donc <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-1e6e09b681ab7b540eec9abdb12e2db2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#68;&#65;&#125;&#123;&#68;&#67;&#125;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#68;&#70;&#125;&#123;&#68;&#69;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"87\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\">Les points A, D et C et F, D et E sont align\u00e9s dans le m\u00eame ordre et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-1e6e09b681ab7b540eec9abdb12e2db2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#68;&#65;&#125;&#123;&#68;&#67;&#125;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#68;&#70;&#125;&#123;&#68;&#69;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"87\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\">D\u2019apr\u00e8s la r\u00e9ciproque du th\u00e9or\u00e8me de Thal\u00e8s, (EC) et (AF) sont parall\u00e8les.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">\t\t<div data-elementor-type=\"section\" data-elementor-id=\"188475\" class=\"elementor elementor-188475\">\n\t\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-inner-section elementor-element elementor-element-692bf02f elementor-section-content-bottom full_width elementor-section-full_width elementor-section-height-min-height elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"692bf02f\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-narrow\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-66 elementor-inner-column elementor-element elementor-element-3124f641 ae-bg-gallery-type-default\" data-id=\"3124f641\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-13b8fcf1 elementor-widget elementor-widget-heading\" data-id=\"13b8fcf1\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">COURS DE MATHS<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-78991b59 elementor-widget elementor-widget-heading\" data-id=\"78991b59\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Nous avons recrut\u00e9 pour vous les<b> meilleurs professeurs particuliers de maths<\/b><\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7d63a247 elementor-widget elementor-widget-heading\" data-id=\"7d63a247\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">S'EXERCER ET APPRENDRE<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-685c251 elementor-align-left elementor-mobile-align-center elementor-widget elementor-widget-button\" data-id=\"685c251\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/cours-particuliers\/maths\/tous-niveaux\/france\/\" target=\"_blank\" class=\"elementor-button-link elementor-button elementor-size-md\" role=\"button\" id=\"CTA_PRD_CP\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Professeur particulier maths<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7a606128 elementor-widget elementor-widget-text-editor\" data-id=\"7a606128\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p style=\"text-align: left;\"><b>Avis Google France <\/b><span style=\"color: #e5a430;\"><b>\u2605\u2605\u2605\u2605\u2605<\/b><\/span><b> 4,8 sur 5<\/b><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-229c063a ae-bg-gallery-type-default\" data-id=\"229c063a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\n<p>&nbsp;<\/p>\n<h2 style=\"text-align: justify;\">Corrig\u00e9 de l&rsquo;exercice 8 : la r\u00e9ciproque du th\u00e9or\u00e8me de Thal\u00e8s<\/h2>\n<p style=\"text-align: justify;\">1) Les points L, A, et C sont align\u00e9s dans le m\u00eame ordre que L, R, et T et (AR) et CT) sont parall\u00e8les.<\/p>\n<p style=\"text-align: justify;\">Donc d\u2019apr\u00e8s le th\u00e9or\u00e8me de Thal\u00e8s <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b308101fbac720ed871e4facda37133c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#76;&#65;&#125;&#123;&#76;&#67;&#125;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#76;&#82;&#125;&#123;&#76;&#84;&#125;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#65;&#82;&#125;&#123;&#67;&#84;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"134\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\">Donc <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-6704e7027414e08ef599edf8b187bfdf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#52;&#44;&#56;&#125;&#123;&#54;&#125;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#76;&#82;&#125;&#123;&#57;&#125;&#32;&#92;&#105;&#102;&#102;&#32;&#76;&#82;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#57;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#52;&#44;&#56;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"241\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\">Donc <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-20c983470a631a00d0c16ad9a6175299_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#76;&#82;&#32;&#61;&#32;&#55;&#44;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"74\" style=\"vertical-align: -4px;\"\/><\/p>\n<p style=\"text-align: justify;\">2) on compare <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d43ada007b8d567aa52f7f981f3f8e6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#76;&#69;&#125;&#123;&#76;&#84;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"27\" style=\"vertical-align: -12px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-ae13edf4f5867c209a141c6079d23c0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#76;&#66;&#125;&#123;&#76;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"27\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-e66e5651884600769e8d56b8d73c6bef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#76;&#69;&#125;&#123;&#76;&#84;&#125;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#51;&#125;&#123;&#57;&#125;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"99\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-346a5ff25f53ca2d49238add47683a7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#76;&#66;&#125;&#123;&#76;&#67;&#125;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#49;&#44;&#53;&#125;&#123;&#51;&#125;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"116\" style=\"vertical-align: -12px;\"\/> donc <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d43ada007b8d567aa52f7f981f3f8e6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#76;&#69;&#125;&#123;&#76;&#84;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"27\" style=\"vertical-align: -12px;\"\/> est diff\u00e9rent de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-ae13edf4f5867c209a141c6079d23c0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#76;&#66;&#125;&#123;&#76;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"27\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: justify;\">Les points B, L, et C sont align\u00e9s dans le m\u00eame ordre que les points E, L, et T<\/p>\n<p style=\"text-align: justify;\">Mais <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d43ada007b8d567aa52f7f981f3f8e6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#76;&#69;&#125;&#123;&#76;&#84;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"27\" style=\"vertical-align: -12px;\"\/> n\u2019est pas \u00e9gal \u00e0 <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-ae13edf4f5867c209a141c6079d23c0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#76;&#66;&#125;&#123;&#76;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"27\" style=\"vertical-align: -12px;\"\/>, Donc d\u2019apr\u00e8s la r\u00e9ciproque du th\u00e9or\u00e8me de Thal\u00e8s, (EB) et (CT) ne sont pas parall\u00e8les.<\/p>\n<p style=\"text-align: justify;\">Comme vous avez pu le constater en traitant ces exercices, pour bien ma\u00eetriser le th\u00e9or\u00e8me de Thal\u00e8s, il est n\u00e9cessaire de ma\u00eetriser d&rsquo;abord le <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-fractions\/\">cours sur les fractions<\/a>. Toutes les notions de maths du sous-test 2 du Tage Mage sont compl\u00e9mentaires, il est donc plus qu&rsquo;important de travailler s\u00e9rieusement chaque notion, commencez par exemple, par revoir les chapitres suivants :<\/p>\n<ul style=\"text-align: justify;\">\n<li style=\"text-align: justify;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-racines-carrees\/\">Cours sur les racines carr\u00e9es<\/a><\/li>\n<li style=\"text-align: justify;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-pourcentages\/\">R\u00e9sum\u00e9 de cours sur les pourcentages<\/a><\/li>\n<li style=\"text-align: justify;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-algebre\/\">Exercices et corrig\u00e9s calcul alg\u00e9brique<\/a><\/li>\n<li style=\"text-align: justify;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-figures-geometriques\/\">Cours g\u00e9om\u00e9trie coll\u00e8ge<\/a><\/li>\n<li><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-racines-carrees\/\">Exercices racines carr\u00e9es coll\u00e8ge<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Exercices corrig\u00e9s th\u00e9or\u00e8me de Thales et sa r\u00e9ciproque R\u00e9sum\u00e9 de cours Exercices et corrig\u00e9s Cours en ligne du Tage Mage Enseign\u00e9 au coll\u00e8ge, le th\u00e9or\u00e8me de Thal\u00e8s est un des th\u00e9or\u00e8mes les plus importants pour le brevet, au m\u00eame titre que le th\u00e9or\u00e8me de Pythagore. Ce th\u00e9or\u00e8me est en effet indispensable pour l&rsquo;\u00e9preuve de brevet [&hellip;]<\/p>\n","protected":false},"author":6,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.2.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Exercices th\u00e9or\u00e8me de Thal\u00e8s et r\u00e9ciproque avec corrig\u00e9s<\/title>\n<meta name=\"description\" content=\"Voici une liste d&#039;exercices corrig\u00e9s sur le th\u00e9or\u00e8me de Thales et sa r\u00e9ciproque permettant d&#039;appliquer le cours sur des cas pratiques.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-theoreme-de-thales\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Exercices th\u00e9or\u00e8me de Thal\u00e8s et r\u00e9ciproque avec corrig\u00e9s\" \/>\n<meta property=\"og:description\" content=\"Voici une liste d&#039;exercices corrig\u00e9s sur le th\u00e9or\u00e8me de Thales et sa r\u00e9ciproque permettant d&#039;appliquer le cours sur des cas pratiques.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-theoreme-de-thales\/\" \/>\n<meta property=\"og:site_name\" content=\"Groupe R\u00e9ussite\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/GroupeReussiteOfficiel\/\" \/>\n<meta property=\"article:modified_time\" content=\"2025-06-02T11:26:44+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2020\/07\/Exercice-thales-rectangle.jpg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@GroupeReussite\" \/>\n<meta name=\"twitter:label1\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data1\" content=\"11 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-theoreme-de-thales\/\",\"url\":\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-theoreme-de-thales\/\",\"name\":\"Exercices th\u00e9or\u00e8me de Thal\u00e8s et r\u00e9ciproque avec corrig\u00e9s\",\"isPartOf\":{\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/#website\"},\"datePublished\":\"2020-07-07T10:22:32+00:00\",\"dateModified\":\"2025-06-02T11:26:44+00:00\",\"description\":\"Voici une liste d'exercices corrig\u00e9s sur le th\u00e9or\u00e8me de Thales et sa r\u00e9ciproque permettant d'appliquer le cours sur des cas pratiques.\",\"breadcrumb\":{\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-theoreme-de-thales\/#breadcrumb\"},\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-theoreme-de-thales\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-theoreme-de-thales\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Accueil\",\"item\":\"https:\/\/groupe-reussite.fr\/ressources\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Th\u00e9or\u00e8me de Thales exercices et corrig\u00e9s\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/#website\",\"url\":\"https:\/\/groupe-reussite.fr\/ressources\/\",\"name\":\"Groupe R\u00e9ussite - Cours particuliers et stages de vacances\",\"description\":\"Stage et Cours particuliers maths, fran\u00e7ais, anglais, informatique, physique chimie\",\"publisher\":{\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/groupe-reussite.fr\/ressources\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"fr-FR\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/#organization\",\"name\":\"Groupe R\u00e9ussite - Cours particuliers et stages de vacances\",\"url\":\"https:\/\/groupe-reussite.fr\/ressources\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2026\/05\/logo-groupe-reussite-carre.png\",\"contentUrl\":\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2026\/05\/logo-groupe-reussite-carre.png\",\"width\":170,\"height\":180,\"caption\":\"Groupe R\u00e9ussite - Cours particuliers et stages de vacances\"},\"image\":{\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/GroupeReussiteOfficiel\/\",\"https:\/\/twitter.com\/GroupeReussite\",\"https:\/\/www.youtube.com\/c\/GroupeReussite\",\"https:\/\/www.instagram.com\/groupe_reussite_officiel\/\",\"https:\/\/fr.linkedin.com\/company\/groupe-reussite\",\"https:\/\/www.tiktok.com\/@groupereussite\",\"https:\/\/fr.pinterest.com\/GroupeReussite\/\",\"https:\/\/www.reddit.com\/user\/Groupe-Reussite\/\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Exercices th\u00e9or\u00e8me de Thal\u00e8s et r\u00e9ciproque avec corrig\u00e9s","description":"Voici une liste d'exercices corrig\u00e9s sur le th\u00e9or\u00e8me de Thales et sa r\u00e9ciproque permettant d'appliquer le cours sur des cas pratiques.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-theoreme-de-thales\/","og_locale":"fr_FR","og_type":"article","og_title":"Exercices th\u00e9or\u00e8me de Thal\u00e8s et r\u00e9ciproque avec corrig\u00e9s","og_description":"Voici une liste d'exercices corrig\u00e9s sur le th\u00e9or\u00e8me de Thales et sa r\u00e9ciproque permettant d'appliquer le cours sur des cas pratiques.","og_url":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-theoreme-de-thales\/","og_site_name":"Groupe R\u00e9ussite","article_publisher":"https:\/\/www.facebook.com\/GroupeReussiteOfficiel\/","article_modified_time":"2025-06-02T11:26:44+00:00","og_image":[{"url":"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2020\/07\/Exercice-thales-rectangle.jpg"}],"twitter_card":"summary_large_image","twitter_site":"@GroupeReussite","twitter_misc":{"Dur\u00e9e de lecture estim\u00e9e":"11 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-theoreme-de-thales\/","url":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-theoreme-de-thales\/","name":"Exercices th\u00e9or\u00e8me de Thal\u00e8s et r\u00e9ciproque avec corrig\u00e9s","isPartOf":{"@id":"https:\/\/groupe-reussite.fr\/ressources\/#website"},"datePublished":"2020-07-07T10:22:32+00:00","dateModified":"2025-06-02T11:26:44+00:00","description":"Voici une liste d'exercices corrig\u00e9s sur le th\u00e9or\u00e8me de Thales et sa r\u00e9ciproque permettant d'appliquer le cours sur des cas pratiques.","breadcrumb":{"@id":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-theoreme-de-thales\/#breadcrumb"},"inLanguage":"fr-FR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-theoreme-de-thales\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-theoreme-de-thales\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Accueil","item":"https:\/\/groupe-reussite.fr\/ressources\/"},{"@type":"ListItem","position":2,"name":"Th\u00e9or\u00e8me de Thales exercices et corrig\u00e9s"}]},{"@type":"WebSite","@id":"https:\/\/groupe-reussite.fr\/ressources\/#website","url":"https:\/\/groupe-reussite.fr\/ressources\/","name":"Groupe R\u00e9ussite - Cours particuliers et stages de vacances","description":"Stage et Cours particuliers maths, fran\u00e7ais, anglais, informatique, physique chimie","publisher":{"@id":"https:\/\/groupe-reussite.fr\/ressources\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/groupe-reussite.fr\/ressources\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"fr-FR"},{"@type":"Organization","@id":"https:\/\/groupe-reussite.fr\/ressources\/#organization","name":"Groupe R\u00e9ussite - Cours particuliers et stages de vacances","url":"https:\/\/groupe-reussite.fr\/ressources\/","logo":{"@type":"ImageObject","inLanguage":"fr-FR","@id":"https:\/\/groupe-reussite.fr\/ressources\/#\/schema\/logo\/image\/","url":"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2026\/05\/logo-groupe-reussite-carre.png","contentUrl":"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2026\/05\/logo-groupe-reussite-carre.png","width":170,"height":180,"caption":"Groupe R\u00e9ussite - Cours particuliers et stages de vacances"},"image":{"@id":"https:\/\/groupe-reussite.fr\/ressources\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/GroupeReussiteOfficiel\/","https:\/\/twitter.com\/GroupeReussite","https:\/\/www.youtube.com\/c\/GroupeReussite","https:\/\/www.instagram.com\/groupe_reussite_officiel\/","https:\/\/fr.linkedin.com\/company\/groupe-reussite","https:\/\/www.tiktok.com\/@groupereussite","https:\/\/fr.pinterest.com\/GroupeReussite\/","https:\/\/www.reddit.com\/user\/Groupe-Reussite\/"]}]}},"_links":{"self":[{"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/pages\/58379"}],"collection":[{"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/comments?post=58379"}],"version-history":[{"count":3,"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/pages\/58379\/revisions"}],"predecessor-version":[{"id":227039,"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/pages\/58379\/revisions\/227039"}],"wp:attachment":[{"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/media?parent=58379"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}