{"id":9950,"date":"2012-10-03T23:21:04","date_gmt":"2012-10-03T22:21:04","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=9950"},"modified":"2022-01-20T21:51:14","modified_gmt":"2022-01-20T21:51:14","slug":"unindo-os-pontos-medios-dos-lados-de-um-quadrilatero-parte-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=9950","title":{"rendered":"Unindo os pontos m\u00e9dios dos lados de um quadril\u00e1tero &#8211; Parte 2"},"content":{"rendered":"<p><ul id='GTTabs_ul_9950' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_9950' class='GTTabs_curr'><a  id=\"9950_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_9950' ><a  id=\"9950_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_9950'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>A que condi\u00e7\u00e3o deve obedecer um quadril\u00e1tero convexo para que, unindo os pontos m\u00e9dios dos lados consecutivos, se obtenha:<\/p>\n<ol>\n<li>um ret\u00e2ngulo;<\/li>\n<li>um quadrado.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_9950' onClick='GTTabs_show(1,9950)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_9950'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ul>\n<li>Recorde: <a href=\"https:\/\/www.acasinhadamatematica.pt\/?p=9916\">Unindo os pontos m\u00e9dios dos lados de um quadril\u00e1tero<\/a><\/li>\n<li>A tarefa FICA AO CUIDADO DO LEITOR \u2013 Utilize a aplica\u00e7\u00e3o apresentada abaixo.<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><script 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is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator, DA=Data Analysis, FI=Function Inspector, PV=Python, macro=Macro View\r\nvar views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 0,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0};\r\nvar applet = new GGBApplet(parameters, '5.0', views);\r\nwindow.onload = function() {applet.inject('ggbApplet')};\r\n<\/script><\/p>\n<\/p>\n<p>\u00a0<a href=\"https:\/\/www.acasinhadamatematica.pt\/?p=9950&amp;page=2\">Ver solu\u00e7\u00e3o<\/a><\/p>\n<p><!--nextpage--><\/p>\n<h5>SOLU\u00c7\u00c3O<\/h5>\n<ol>\n<li>Quando o quadril\u00e1tero dado tem diagonais perpendiculares, os pontos m\u00e9dios dos lados consecutivos definem um ret\u00e2ngulo.<br \/>\n<table border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" colspan=\"2\">EXEMPLOS<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s1.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"9958\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=9958\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s1.jpg\" data-orig-size=\"412,248\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;AMMA&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1349306162&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Ret\u00e2ngulo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s1.jpg\" class=\"aligncenter  wp-image-9958\" title=\"Ret\u00e2ngulo\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s1.jpg\" alt=\"\" width=\"330\" height=\"198\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s1.jpg 412w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s1-300x180.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s1-150x90.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s1-400x240.jpg 400w\" sizes=\"auto, (max-width: 330px) 100vw, 330px\" \/><\/a><\/td>\n<td><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s2.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"9959\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=9959\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s2.jpg\" data-orig-size=\"246,330\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;AMMA&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1349305928&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Ret\u00e2ngulo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s2.jpg\" class=\"aligncenter  wp-image-9959\" title=\"Ret\u00e2ngulo\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s2.jpg\" alt=\"\" width=\"197\" height=\"264\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s2.jpg 246w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s2-223x300.jpg 223w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s2-111x150.jpg 111w\" sizes=\"auto, (max-width: 197px) 100vw, 197px\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>Quando o quadril\u00e1tero dado tem diagonais perpendiculares e iguais, os pontos m\u00e9dios dos lados consecutivos definem um quadrado.<br \/>\n<table border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" colspan=\"2\">EXEMPLOS<\/td>\n<\/tr>\n<tr>\n<td>\u00a0<img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"9960\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=9960\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s3.jpg\" data-orig-size=\"289,288\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;AMMA&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1349305606&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Quadrado\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s3.jpg\" class=\"aligncenter  wp-image-9960\" title=\"Quadrado\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s3.jpg\" alt=\"\" width=\"231\" height=\"230\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s3.jpg 289w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s3-150x150.jpg 150w\" sizes=\"auto, (max-width: 231px) 100vw, 231px\" \/><\/td>\n<td>\u00a0<img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"9961\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=9961\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s4.jpg\" data-orig-size=\"331,330\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;AMMA&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1349305858&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Quadrado\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s4.jpg\" class=\"aligncenter  wp-image-9961\" title=\"Quadrado\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s4.jpg\" alt=\"\" width=\"265\" height=\"264\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s4.jpg 331w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s4-150x150.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/s4-300x300.jpg 300w\" sizes=\"auto, (max-width: 265px) 100vw, 265px\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_9950' onClick='GTTabs_show(0,9950)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A que condi\u00e7\u00e3o deve obedecer um quadril\u00e1tero convexo para que, unindo os pontos m\u00e9dios dos lados consecutivos, se obtenha: um ret\u00e2ngulo; um quadrado. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20775,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[321,97,322],"tags":[429,67,430],"series":[],"class_list":["post-9950","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-10-o-ano","category-aplicando","category-modulo-inicial","tag-10-o-ano","tag-geometria","tag-modulo-inicial"],"views":4688,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/10V1Pag035-12_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9950","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=9950"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9950\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20775"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9950"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9950"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9950"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=9950"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}