{"id":1551,"date":"2016-08-16T23:42:52","date_gmt":"2016-08-16T22:42:52","guid":{"rendered":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/?p=1551"},"modified":"2018-02-17T02:05:53","modified_gmt":"2018-02-17T01:05:53","slug":"mise-en-equation-avec-thales","status":"publish","type":"post","link":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/mise-en-equation-avec-thales\/","title":{"rendered":"Mise en \u00e9quation avec Thal\u00e8s"},"content":{"rendered":"<p>On consid\u00e8re un triangle OAB tel que : OA = 12 cm, OB = 8 cm et AB = 6 cm.<\/p>\n<p>M est un point du segment [OA].\u00a0 La droite (d), parall\u00e8le \u00e0 (AB) passant par M, coupe le segment [OB] en N.<\/p>\n<p>On se propose de d\u00e9terminer la longueur OM pour que le p\u00e9rim\u00e8tre du triangle OMN soit \u00e9gal \u00e0 celui du trap\u00e8ze MNBA.<\/p>\n<ul>\n<li>Faire une figure \u00ab \u00e0 la main \u00bb sur une feuille.<\/li>\n<li>R\u00e9aliser la figure \u00e0 l\u2019aide de Geoplan, puis utiliser cette figure pour conjecturer une valeur approch\u00e9e de la longueur OM r\u00e9pondant au probl\u00e8me.<\/li>\n<li>D\u00e9termination de la valeur exacte de OM par le calcul :<\/li>\n<\/ul>\n<p>On pose OM = <em>x<\/em>.<\/p>\n<ol>\n<li>Exprimer les distances ON et MN en fonction de <em>x<\/em>.<\/li>\n<li>En d\u00e9duire les p\u00e9rim\u00e8tres du triangle OMN et du trap\u00e8ze MNBA en fonction de <em>x<\/em>.<\/li>\n<li>En d\u00e9duire la valeur exacte de <em>x<\/em> r\u00e9pondant au probl\u00e8me.<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<p>Travail \u00e0 rendre :<\/p>\n<ul>\n<li>La figure faite \u00e0 la main<\/li>\n<li>Une impression de la figure et du texte de la figure (\u00c9diter \u00e8 Texte figure)<\/li>\n<li>La justification alg\u00e9brique.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p><a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2017\/06\/mise_en_equation_thales.docx\">Fiche \u00e9l\u00e8ve Mise en \u00e9quation avec Thal\u00e8s word<\/a><\/p>\n<p><a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2017\/06\/mise_en_equation_thales.pdf\">Fiche \u00e9l\u00e8ve Mise en \u00e9quation avec Thal\u00e8s pdf<\/a><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><em><br \/>\n<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>On consid\u00e8re un triangle OAB tel que : OA = 12 cm, OB = 8 cm et AB = 6 cm. M est un point du segment [OA].\u00a0 La droite (d), parall\u00e8le \u00e0 (AB) passant par M, coupe le segment [OB] en N. On se propose de d\u00e9terminer la longueur OM pour que le p\u00e9rim\u00e8tre &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/mise-en-equation-avec-thales\/\">Lire la suite<\/a><\/p>\n","protected":false},"author":351,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"footnotes":""},"categories":[23,22,14],"tags":[],"class_list":["post-1551","post","type-post","status-publish","format-standard","hentry","category-seconde","category-lycee","category-numerique","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/1551","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/users\/351"}],"replies":[{"embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/comments?post=1551"}],"version-history":[{"count":4,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/1551\/revisions"}],"predecessor-version":[{"id":2787,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/1551\/revisions\/2787"}],"wp:attachment":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/media?parent=1551"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/categories?post=1551"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/tags?post=1551"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}