{"id":1505,"date":"2016-08-16T22:16:28","date_gmt":"2016-08-16T21:16:28","guid":{"rendered":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/?p=1505"},"modified":"2018-02-17T02:06:17","modified_gmt":"2018-02-17T01:06:17","slug":"demonstration-puzzle","status":"publish","type":"post","link":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/demonstration-puzzle\/","title":{"rendered":"D\u00e9monstration Puzzle"},"content":{"rendered":"<p><strong><em>\u00c9nonc\u00e9\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/em><\/strong><\/p>\n<p>ABC est un triangle rectangle en A.<\/p>\n<p>H est le pied de la hauteur issue de A dans le triangle ABC.<\/p>\n<p>I et J sont les milieux respectifs de [BH] et [AH].<\/p>\n<p>D\u00e9montrer que les droites (AI) et (CJ) sont perpendiculaires.<\/p>\n<p>&nbsp;<\/p>\n<p><strong><em>Reconstituer la d\u00e9monstration \u00e0 l\u2019aide des \u00e9l\u00e9ments de phrases suivants\u00a0 :\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/em><\/strong><\/p>\n<ul>\n<li>donc les droites (AI) et (CJ) sont perpendiculaires.<\/li>\n<li>on en d\u00e9duit que la droite (IJ) est la hauteur issue de I dans le triangle ACI.<\/li>\n<li>on sait que ABC est un triangle rectangle en A, donc les droites (AB) et (AC) sont perpendiculaires.<\/li>\n<li>donc la droite (IJ) est perpendiculaire \u00e0 la droite (AC).<\/li>\n<li>dans le triangle ABH, on a I milieu de [BH] et J milieu de [AH].<\/li>\n<li>de plus la droite (AH) est la hauteur issue de A dans le triangle ACI.<\/li>\n<li>si deux droites sont parall\u00e8les, alors toute perpendiculaire \u00e0 l\u2019une est perpendiculaire \u00e0 l\u2019autre.<\/li>\n<li>donc les droites (IJ) et (AB) sont parall\u00e8les.<\/li>\n<li>donc J, point d\u2019intersection des droites (AH) et (IJ) est<\/li>\n<li>on en d\u00e9duit que la droite (CJ) est la hauteur issue de C dans le triangle ACI.<\/li>\n<li>l\u2019orthocentre du triangle ACI.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p><a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/08\/demonstration_puzzle.docx\">Fiche \u00e9l\u00e8ve D\u00e9monstration Puzzle word<\/a><\/p>\n<p><a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/08\/demonstration_puzzle.pdf\">Fiche \u00e9l\u00e8ve D\u00e9monstration Puzzle pdf<\/a><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00c9nonc\u00e9\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ABC est un triangle rectangle en A. H est le pied de la hauteur issue de A dans le triangle ABC. I et J sont les milieux respectifs de [BH] et [AH]. D\u00e9montrer que les droites (AI) et (CJ) sont perpendiculaires. &nbsp; Reconstituer la d\u00e9monstration \u00e0 l\u2019aide des \u00e9l\u00e9ments de phrases suivants\u00a0 :\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 donc &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/demonstration-puzzle\/\">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],"tags":[],"class_list":["post-1505","post","type-post","status-publish","format-standard","hentry","category-seconde","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/1505","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=1505"}],"version-history":[{"count":1,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/1505\/revisions"}],"predecessor-version":[{"id":1506,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/1505\/revisions\/1506"}],"wp:attachment":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/media?parent=1505"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/categories?post=1505"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/tags?post=1505"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}