{"id":4750,"date":"2010-10-27T19:27:59","date_gmt":"2010-10-27T18:27:59","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=4750"},"modified":"2022-01-14T23:12:39","modified_gmt":"2022-01-14T23:12:39","slug":"rascunho-20","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=4750","title":{"rendered":"Soma dos \u00e2ngulos de um quadril\u00e1tero"},"content":{"rendered":"<p><ul id='GTTabs_ul_4750' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_4750' class='GTTabs_curr'><a  id=\"4750_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_4750' ><a  id=\"4750_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_4750'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Prova que a soma das amplitudes dos \u00e2ngulos internos de um quadril\u00e1tero \u00e9 360\u00ba.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_4750' onClick='GTTabs_show(1,4750)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_4750'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Consideremos o quadril\u00e1tero [ABCD]:<\/p>\n<p style=\"text-align: center;\"><script src=\"https:\/\/cdn.geogebra.org\/apps\/deployggb.js\"><\/script>\r\n<div id=\"ggbApplet\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet\",\r\n\"width\":740,\r\n\"height\":398,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 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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': 1,'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>Tracemos a diagonal [AC].<br \/>\nO quadril\u00e1tero \u00e9 dividido em dois tri\u00e2ngulos, [ABC] e [ACD].<\/p>\n<ul>\n<li>A soma das amplitudes dos \u00e2ngulos internos do tri\u00e2ngulo [ABC] \u00e9 180\u00ba;<\/li>\n<li>A soma das amplitudes dos \u00e2ngulos internos do tri\u00e2ngulo [ACD] \u00e9 180\u00ba.<\/li>\n<\/ul>\n<p>Logo, a soma das amplitudes dos \u00e2ngulos internos do quadril\u00e1tero [ABCD] \u00e9 360\u00ba.<\/p>\n<p>\\[\\begin{array}{*{35}{l}}<br \/>\n\\hat{A}+\\hat{B}+\\hat{C}+\\hat{D} &amp; = &amp; ({{{\\hat{a}}}_{1}}+{{{\\hat{a}}}_{2}})+\\hat{b}+({{{\\hat{c}}}_{1}}+{{{\\hat{c}}}_{2}})+\\hat{d}\u00a0 \\\\<br \/>\n{} &amp; = &amp; ({{{\\hat{a}}}_{1}}+\\hat{b}+{{{\\hat{c}}}_{1}})+({{{\\hat{a}}}_{2}}+{{{\\hat{c}}}_{2}}+\\hat{d})\u00a0 \\\\<br \/>\n{} &amp; = &amp; 180{}^\\text{o}+180{}^\\text{o}\u00a0 \\\\<br \/>\n{} &amp; = &amp; 360{}^\\text{o}\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p><br class=\"spacer_\" \/><br \/>\n<strong>Qual a soma das amplitudes dos \u00e2ngulos internos de um pent\u00e1gono?<\/strong><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_4750' onClick='GTTabs_show(0,4750)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Prova que a soma das amplitudes dos \u00e2ngulos internos de um quadril\u00e1tero \u00e9 360\u00ba. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":19234,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,102],"tags":[424,105],"series":[],"class_list":["post-4750","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-do-espaco-ao-plano","tag-8-o-ano","tag-angulos"],"views":2954,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat76.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/4750","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=4750"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/4750\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19234"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4750"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4750"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4750"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=4750"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}