{"id":1990,"date":"2016-09-24T21:23:55","date_gmt":"2016-09-24T20:23:55","guid":{"rendered":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/?p=1990"},"modified":"2023-05-23T15:35:08","modified_gmt":"2023-05-23T14:35:08","slug":"alignement","status":"publish","type":"post","link":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/alignement\/","title":{"rendered":"Alignement"},"content":{"rendered":"<h2>Objectifs<\/h2>\n<ul>\n<li>\u00a0Utiliser ses connaissances math\u00e9matiques pour r\u00e9aliser une figure \u00e0 l&#8217;aide d&#8217;un logiciel de g\u00e9om\u00e9trie dynamique<\/li>\n<li>\u00a0Utiliser le logiciel pour \u00e9mettre une conjecture<\/li>\n<li>\u00a0Mettre en place une d\u00e9marche de d\u00e9monstration<\/li>\n<\/ul>\n<h2>Pr\u00e9requis<\/h2>\n<ul>\n<li>\u00a0Utilisation basique d\u2019un logiciel de g\u00e9om\u00e9trie dynamique<\/li>\n<li>\u00a0\u00c9quations de droites ou vecteurs colin\u00e9aires<\/li>\n<\/ul>\n<h2>\u00c9nonc\u00e9<\/h2>\n<table style=\"height: 186px\" width=\"725\">\n<tbody>\n<tr>\n<td>Soit ABCD un carr\u00e9 de c\u00f4t\u00e9 4\u00a0cm. Soit I \u00e0 l\u2019int\u00e9rieur du carr\u00e9\u00a0tel\u00a0que<\/p>\n<p>AIB soit un triangle isoc\u00e8le en\u00a0I.<\/p>\n<p>Soit L \u00e0 l\u2019ext\u00e9rieur du carr\u00e9 tel que CBL soit un triangle isoc\u00e8le\u00a0en\u00a0L avec CL = AI.<\/p>\n<p>Les points D, I et L peuvent-ils \u00eatre align\u00e9s\u00a0?<\/p>\n<p>&nbsp;<\/td>\n<td width=\"231\">\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1991\" src=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/09\/Alignement.jpg\" alt=\"alignement\" width=\"291\" height=\"177\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>D\u00e9roulement de la s\u00e9quence<\/h2>\n<p>En salle informatique, puis travail sur papier.<\/p>\n<ul>\n<li>A l\u2019aide d\u2019un logiciel de g\u00e9om\u00e9trie dynamique les \u00e9l\u00e8ves construisent une figure r\u00e9pondant \u00e0 l\u2019\u00e9nonc\u00e9\u00a0; ils peuvent alors conjecturer \u00e0 l\u2019aide de diff\u00e9rents affichages (longueurs, angles, \u2026) la nature des triangles AIB et CBL lorsque l\u2019alignement des points D, I et L est r\u00e9alis\u00e9<\/li>\n<li>Ils doivent ensuite d\u00e9montrer la conjecture\u00a0; pour cela l\u2019introduction d\u2019un rep\u00e8re orthonorm\u00e9 bien choisi permet d\u2019utiliser soit des \u00e9quations de droites, soit des coordonn\u00e9es de vecteurs.<\/li>\n<\/ul>\n<h2>Documents<\/h2>\n<ul>\n<li><a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/09\/alignement_eleve_geoplan.zip\">Figures g\u00e9oplan \u00e9l\u00e8ve Alignement<\/a><\/li>\n<li><a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/09\/alignement_prof_geoplan.zip\">Figure g\u00e9oplan professeur Alignement<\/a><\/li>\n<li><a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/09\/alignement_prof_geogebra.zip\">Figure g\u00e9og\u00e9bra professeur Alignement<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Objectifs \u00a0Utiliser ses connaissances math\u00e9matiques pour r\u00e9aliser une figure \u00e0 l&#8217;aide d&#8217;un logiciel de g\u00e9om\u00e9trie dynamique \u00a0Utiliser le logiciel pour \u00e9mettre une conjecture \u00a0Mettre en place une d\u00e9marche de d\u00e9monstration Pr\u00e9requis \u00a0Utilisation basique d\u2019un logiciel de g\u00e9om\u00e9trie dynamique \u00a0\u00c9quations de droites ou vecteurs colin\u00e9aires \u00c9nonc\u00e9 Soit ABCD un carr\u00e9 de c\u00f4t\u00e9 4\u00a0cm. Soit I \u00e0 &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/alignement\/\">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-1990","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\/1990","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=1990"}],"version-history":[{"count":4,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/1990\/revisions"}],"predecessor-version":[{"id":1998,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/1990\/revisions\/1998"}],"wp:attachment":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/media?parent=1990"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/categories?post=1990"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/tags?post=1990"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}