{"id":16676,"date":"2023-03-20T13:47:49","date_gmt":"2023-03-20T12:47:49","guid":{"rendered":"https:\/\/college-willy-ronis.fr\/maths\/?p=16676"},"modified":"2023-03-20T14:08:09","modified_gmt":"2023-03-20T13:08:09","slug":"chapitre-17-la-reciproque-du-theoreme-de-thales","status":"publish","type":"post","link":"https:\/\/college-willy-ronis.fr\/maths\/chapitre-17-la-reciproque-du-theoreme-de-thales\/","title":{"rendered":"Chapitre 17 : La r\u00e9ciproque du th\u00e9or\u00e8me de Thal\u00e8s"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"16676\" class=\"elementor elementor-16676\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-682277ef elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"682277ef\" data-element_type=\"section\" 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d=\"M154.5,26.7c-0.1-0.1-4.6,0.3-7.2,0c-7.3-0.7-17-3.2-16.6-2.9c0.4,0.3,13.7,3.1,17,3.3\tC152.6,27.5,154.6,26.8,154.5,26.7z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M41.9,19.3c0,0,1.2-0.3,2.9-0.1c1.7,0.2,5.8,0.9,8.2,0.7c4.2-0.4,7.4-2.7,7-2.6\tc-0.4,0-4.3,2.2-8.6,1.9c-1.8-0.1-5.1-0.5-6.7-0.4S41.9,19.3,41.9,19.3z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M75.5,12.6c0.2,0.1,2-0.8,4.3-1.1c2.3-0.2,2.1-0.3,2.1-0.5c0-0.1-1.8-0.4-3.4,0\tC76.9,11.5,75.3,12.5,75.5,12.6z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M15.6,13.2c0-0.1,4.3,0,6.7,0.5c2.4,0.5,5,1.9,5,2c0,0.1-2.7-0.8-5.1-1.4\tC19.9,13.7,15.7,13.3,15.6,13.2z\"\/>\n<\/svg>\t\t<\/div>\n\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-5d0bc302\" data-id=\"5d0bc302\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-654d4d51 elementor-widget elementor-widget-heading\" data-id=\"654d4d51\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Chapitre 17<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-43ddd515 elementor-widget elementor-widget-heading\" data-id=\"43ddd515\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">La r\u00e9ciproque du th\u00e9or\u00e8me de Thal\u00e8s<\/h1>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6b0067f elementor-widget elementor-widget-text-editor\" data-id=\"6b0067f\" 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\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-c9f40c0\" data-id=\"c9f40c0\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5fd645cf elementor-widget elementor-widget-image\" data-id=\"5fd645cf\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"192\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/02\/cours-maths-4eme.png\" class=\"attachment-medium size-medium wp-image-15214\" alt=\"Cours de math\u00e9matiques de 4\u00e8me\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-f34dc8e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f34dc8e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-198e363\" data-id=\"198e363\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-94fa771 elementor-widget elementor-widget-spacer\" data-id=\"94fa771\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-65b2f06 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"65b2f06\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ebe0063\" data-id=\"ebe0063\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a1b3eae elementor-widget elementor-widget-heading\" data-id=\"a1b3eae\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Chapitre 17 : La r\u00e9ciproque du th\u00e9or\u00e8me de Thal\u00e8s<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-96add89 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"96add89\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b495cd0\" data-id=\"b495cd0\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-10e68ef elementor-widget elementor-widget-spacer\" data-id=\"10e68ef\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-32398ea elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"32398ea\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0702a6a\" data-id=\"0702a6a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5dd87d7 elementor-widget elementor-widget-text-editor\" data-id=\"5dd87d7\" 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<p><strong>Propri\u00e9t\u00e9 :<\/strong> Si deux droites $(AB)$ et $(AC)$ sont s\u00e9cantes en un point $A$,<br \/>si les points $A, M, B$ et les points $A, N, C$ sont align\u00e9s dans le m\u00eame ordre, et si $ \\dfrac{AM}{AB}=\\dfrac{AN}{AC} $ alors les droites $(BC)$ et $(MN)$ sont parall\u00e8les.<\/p><p>\u00a0<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7144f94 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7144f94\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-67568aa\" data-id=\"67568aa\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-efebd6c elementor-widget elementor-widget-image\" data-id=\"efebd6c\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"385\" height=\"360\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/03\/reciproque-thales-4eme-1.png\" class=\"attachment-large size-large wp-image-16680\" alt=\"\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/03\/reciproque-thales-4eme-1.png 385w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/03\/reciproque-thales-4eme-1-300x281.png 300w\" sizes=\"auto, (max-width: 385px) 100vw, 385px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6f2f671 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6f2f671\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2dfb37f\" data-id=\"2dfb37f\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1646769 elementor-widget elementor-widget-text-editor\" data-id=\"1646769\" 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<p><strong>Remarque :<\/strong> Ce th\u00e9or\u00e8me permet de prouver que deux droites sont parall\u00e8les.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0a1a78c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0a1a78c\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c87cbe5\" data-id=\"c87cbe5\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c2a872e elementor-widget elementor-widget-text-editor\" data-id=\"c2a872e\" 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<p><strong>Exemple :<\/strong> Avec les donn\u00e9es de la figure ci-dessous, d\u00e9montrer que $(OL)$ est parall\u00e8le \u00e0 $(UP)$.<\/p><ul><li><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-16681 size-full\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/03\/reciproque-thales-4eme-2.png\" alt=\"\" width=\"496\" height=\"376\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/03\/reciproque-thales-4eme-2.png 496w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/03\/reciproque-thales-4eme-2-300x227.png 300w\" sizes=\"auto, (max-width: 496px) 100vw, 496px\" \/><br \/>\\[<br \/>\\left.<br \/>\\begin{array}{ccccc}<br \/>\\dfrac{IO}{IP}&amp;=&amp;\\dfrac{6}{10,5}&amp;=&amp;\\dfrac{4}{7}\\\\<br \/>\\\\<br \/>\\dfrac{IL}{IU}&amp;=&amp;\\dfrac{4}{7}&amp;&amp;\\\\<br \/>\\end{array}<br \/>\\right\\}\\mbox{Donc}~~\\dfrac{IO}{IP}=\\dfrac{IL}{IU}<br \/>\\]<\/li><li>Les droites $(IP)$ et $(IU)$ sont s\u00e9cantes en $I$.<\/li><li>Les points $I, O, P$ et $I,L,U$ sont align\u00e9s dans le m\u00eame ordre.<br \/>D\u2019apr\u00e8s la r\u00e9ciproque du th\u00e9or\u00e8me de Thal\u00e8s, on en d\u00e9duit que $(OL)$ est parall\u00e8le \u00e0 $(UP)$.<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5d23f8c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5d23f8c\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b64e922\" data-id=\"b64e922\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-cee7de5 elementor-widget elementor-widget-video\" data-id=\"cee7de5\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/U9XX5w8FeOI&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a86cc67 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a86cc67\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7fb20e1\" data-id=\"7fb20e1\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-939552d elementor-widget elementor-widget-spacer\" data-id=\"939552d\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5f69481 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5f69481\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4b560c0\" data-id=\"4b560c0\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0bbf221 elementor-button-info elementor-align-center elementor-widget elementor-widget-button\" data-id=\"0bbf221\" 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 class=\"elementor-button elementor-button-link elementor-size-xl\" href=\"https:\/\/nuage02.apps.education.fr\/index.php\/s\/7PgW2YbN68JF7Bo\" target=\"_blank\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-icon elementor-align-icon-left\">\n\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-arrow-alt-circle-right\"><\/i>\t\t\t<\/span>\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Exercices corrig\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\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-77ba960 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"77ba960\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-01e95c1\" data-id=\"01e95c1\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-dbc07c3 elementor-widget elementor-widget-spacer\" data-id=\"dbc07c3\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Chapitre 17 La r\u00e9ciproque du th\u00e9or\u00e8me de Thal\u00e8s Chapitre 17 : La r\u00e9ciproque du th\u00e9or\u00e8me de Thal\u00e8s Propri\u00e9t\u00e9 : Si deux droites $(AB)$ et $(AC)$ sont s\u00e9cantes en un point $A$,si les points $A, M, B$ et les points $A, N, C$ sont align\u00e9s dans le m\u00eame ordre, et si $ dfrac{AM}{AB}=dfrac{AN}{AC} $ alors les [&hellip;]<\/p>\n","protected":false},"author":7440,"featured_media":16677,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"site-sidebar-layout":"default","site-content-layout":"page-builder","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[39],"tags":[],"class_list":["post-16676","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cours-et-exercices-4eme"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Chapitre 17 : La r\u00e9ciproque du th\u00e9or\u00e8me de Thal\u00e8s<\/title>\n<meta name=\"description\" content=\"Cours de math\u00e9matiques de 4\u00e8me du coll\u00e8ge Willy Ronis sur la r\u00e9ciproque du th\u00e9or\u00e8me de thal\u00e8s, des vid\u00e9os, les exercices corrig\u00e9s...\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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