{"id":6832,"date":"2013-07-13T21:12:17","date_gmt":"2013-07-14T00:12:17","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=6832"},"modified":"2024-11-26T23:21:49","modified_gmt":"2024-11-27T02:21:49","slug":"brincando-com-geometria-soma-dos-angulos-internos-de-um-triangulo","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/brincando-com-geometria-soma-dos-angulos-internos-de-um-triangulo\/","title":{"rendered":".Sala de Estudo:  Soma dos \u00e2ngulos internos de um tri\u00e2ngulo"},"content":{"rendered":"<hr style=\"height:1px;background-color:#8B5A2B; margin-top: 6px; margin-bottom: 6px; border: 0 none\"\/>\n<hr style=\"height:1px;background-color:#8B5A2B; margin-top: 6px; margin-bottom: 6px; border: 0 none\"\/>\n<p style=\"text-align:center; color: #8B5A2B; font-family: Georgia, Times, 'Times New Roman', serif; margin:10px;line-height:40px; font-size: 30px; \"><strong>Soma dos \u00e2ngulos internos de um tri\u00e2ngulo<\/strong><\/p>\n<hr style=\"height:1px;background-color:#8B5A2B; margin-top: 6px; margin-bottom: 6px; border: 0 none\"\/>\n<hr style=\"height:1px;background-color:#8B5A2B; margin-top: 6px; margin-bottom: 6px; border: 0 none\"\/>\n<p style=\"margin:50px\">\n<div style=\"border: 8px double #8B5A2B; padding: 5px;\">\n<table style=\" height:auto; margin-left: auto; margin-right: auto; width:640px;\">\n<tr>\n<td style=\"border: 1px solid #ffffff\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1001 alignright\" style=\"border: 0px;\" alt=\"\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/01\/menino.jpg\" width=\"95\" height=\"115\" \/><\/td>\n<td  style=\"border: 1px solid  #ffffff\">\n<p style=\"text-align: justify; padding: 10px; border-style: dotted; border-color :#1C1C1C; border-width :thin; width:520px;background-color: #CDBA96;\"><span style=\"color: #1C1C1C; font-family: Georgia, Times, 'Times New Roman', serif; font-size: 16px;\">Qual \u00e9 a soma das medidas dos \u00e2ngulos internos de um dado tri\u00e2ngulo?<br \/>\nVoc\u00ea n\u00e3o sabe?<br \/>\nN\u00e3o faz mal, vamos calcul\u00e1-la juntos.<\/span><\/p>\n<p><\/td>\n<\/tr>\n<\/table>\n<table style=\" height:auto; margin-left: auto; margin-right: auto; width:514px;\">\n<tr>\n<td style=\"border: 1px solid  #ffffff;\">\n<p style=\"text-align: justify; padding: 15px; border-style: dotted; border-color :#1C1C1C; border-width :thin; width:400px;background-color: #CDBA96;\"><span style=\"color: #000000; font-family: Georgia, Times, 'Times New Roman', serif; font-size: 16px;\">Se necess\u00e1rio, veja algumas defini\u00e7\u00f5es <a href=\"http:\/\/clubes.obmep.org.br\/blog\/?p=110390\" title=\"Visite esta sala!\" target=\"_blank\"><span style=\"color: #FFFAFA; font-family: verdana, Arial, Helvetica, sans-serif; font-size: 14px;\"><strong>AQUI<\/strong><\/span><\/a>, para que voc\u00ea n\u00e3o fique com d\u00favidas&#8230;.<\/span><\/p>\n<p><\/td>\n<td style=\"border: 1px solid #ffffff\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/02\/carinha3.jpg\" style=\"border: 0px;\" alt=\"carinha3\" width=\"80\" height=\"80\" class=\"alignleft size-full wp-image-3064\" \/><\/td>\n<\/tr>\n<\/table>\n<p style=\"margin:10px\">\n<div style=\"border: 1px solid #000080; width: 650px; height: 420px; background-color: #d2b48c; margin-left: auto; margin-right: auto;\">\n<p style=\"margin:20px\">\n<p>\t<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/07\/reformada02.jpg\" style=\"border: 0px;\" alt=\"reformada02\" width=\"620\" height=\"430\" class=\"aligncenter size-full wp-image-38907\" \/>\n\t<\/div>\n<p style=\"margin:40px\">\n<hr style=\"height:3px; width:98%;background-color:#8B5A2B; margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px; width:95%;background-color:#8B5A2B; margin-top:8px; margin-bottom: 8px; border: 0 none\"\/>\n<p style=\"margin:40px\">\n<table style=\" height:auto; margin-left: auto; margin-right: auto;width:640px;\">\n<tr>\n<td style=\"border: 1px solid #ffffff\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1001 alignright\" style=\"border: 0px;\" alt=\"\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/01\/menino.jpg\" width=\"95\" height=\"115\" \/><\/td>\n<td  style=\"border: 1px solid  #ffffff\">\n<p style=\"text-align: justify; padding: 10px; border-style: dotted; border-color :#1C1C1C; border-width :thin; width:520px;background-color: #CDBA96;\"><span style=\"color: #1C1C1C; font-family: Georgia, Times, 'Times New Roman', serif; font-size: 16px;\">(1) Trace uma reta <em><strong>r<\/strong><\/em> passando por um dos v\u00e9rtices do tri\u00e2ngulo e paralela ao lado oposto do v\u00e9rtice escolhido.<br \/>\nProlongue, tamb\u00e9m, os lados adjacentes do v\u00e9rtice escolhido. <\/span><\/p>\n<\/td>\n<\/tr>\n<\/table>\n<p style=\"margin:10px\">\n<div style=\"border: 1px solid #000080; width: 650px; height: 420px; background-color: #d2b48c; margin-left: auto; margin-right: auto;\">\n<p style=\"margin:20px\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/07\/L2.png\" style=\"border: 0px;\" alt=\"L2\" width=\"620\" height=\"430\" class=\"aligncenter size-full wp-image-16933\" \/><\/div>\n<p style=\"margin:40px\">\n<hr style=\"height:3px; width:98%;background-color:#8B5A2B; border: 0 none\"\/>\n<p style=\"margin:40px\">\n<table style=\" height:auto; margin-left: auto; margin-right: auto; width: 647px;\">\n<tr>\n<td style=\"border: 1px solid #ffffff\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1001 alignright\" style=\"border: 0px;\" alt=\"\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/01\/menino.jpg\" width=\"95\" height=\"115\" \/><\/td>\n<td  style=\"border: 1px solid  #ffffff\">\n<p style=\"text-align: justify; padding: 10px; border-style: dotted; border-color :#1C1C1C; border-width :thin; width:510px;background-color: #CDBA96;\"><span style=\"color: #1C1C1C; font-family: Georgia, Times, 'Times New Roman', serif; font-size: 16px;\">(2) Observe os novos \u00e2ngulos que apareceram.<br \/>\nCompare as medidas \u03b1\u2032, \u03b2\u2032 e \u03b3\u2032 desses \u00e2ngulos com as medidas dos \u00e2ngulos internos do tri\u00e2ngulo em quest\u00e3o.<\/span><\/p>\n<\/td>\n<\/tr>\n<\/table>\n<p style=\"margin:10px\">\n<div style=\"border: 1px solid #000080; width: 650px; height: 420px; background-color: #d2b48c; margin-left: auto; margin-right: auto;\">\n<p style=\"margin:20px\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/07\/L31.png\" style=\"border: 0px;\"  alt=\"L3\" width=\"620\" height=\"430\" class=\"aligncenter size-full wp-image-16934\" \/><\/div>\n<p style=\"margin:40px\">\n<hr style=\"height:3px; width:98%;background-color:#8B5A2B; border: 0 none\"\/>\n<p style=\"margin:40px\">\n<table style=\" height:auto; margin-left: auto; margin-right: auto;316px;\">\n<tr>\n<td style=\"border: 1px solid #ffffff\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1001 alignright\" style=\"border: 0px;\" alt=\"\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/01\/menino.jpg\" width=\"95\" height=\"115\" \/><\/td>\n<td  style=\"border: 1px solid  #ffffff\">\n<p style=\"text-align: center; padding: 5px; border-style: dotted; border-color :#1C1C1C; border-width :thin; width:200px;background-color: #CDBA96;\"><span style=\"color: #1C1C1C; font-family: Georgia, Times, 'Times New Roman', serif; font-size: 16px; line-height: 25px;\">(3) <strong>Dica final<\/strong>:<br \/>\nCalcule &nbsp;\u03b1 \u2032&nbsp;+&nbsp; \u03b2 \u2032&nbsp;+&nbsp;\u03b3 \u2032.<\/span><\/p>\n<\/td>\n<\/tr>\n<\/table>\n<p style=\"margin:10px\">\n<div style=\"border: 1px solid #000080; width: 650px; height: 420px; background-color: #d2b48c; margin-left: auto; margin-right: auto;\">\n<p style=\"margin:20px\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/07\/L44.png\" style=\"border: 0px;\" alt=\"L44\" width=\"620\" height=\"430\" class=\"aligncenter size-full wp-image-16936\" \/>\n<\/div>\n<p style=\"margin:40px\">\n<hr style=\"height:3px; width:98%;background-color:#8B5A2B;  margin-top: 8px; margin-bottom: 8px;border: 0 none\"\/>\n<p style=\"margin:40px\">\n<table style=\" height:auto; margin-left: auto; margin-right: auto;width:640px;\">\n<tr>\n<td style=\"border: 1px solid #ffffff\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1001 alignright\" style=\"border: 0px;\" alt=\"\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/01\/menino.jpg\" width=\"95\" height=\"115\" \/><\/td>\n<td  style=\"border: 1px solid  #ffffff\">\n<p style=\"text-align: justify; padding: 10px; border-style: dotted; border-color :#1C1C1C; border-width:thin; width:510px; background-color: #CDBA96;\"><span style=\"color: #1C1C1C; font-family: Georgia, Times, 'Times New Roman', serif;  font-size: 16px;\">(4) Com as dicas dadas, voc\u00ea conseguiu mostrar que a soma, em graus, das medidas dos \u00e2ngulos internos de um tri\u00e2ngulo \u00e9 [tex] 180^\\circ[\/tex]. Confira na planilha din\u00e2mica abaixo alguns casos particulares desse resultado.<\/span><\/p>\n<\/td>\n<\/tr>\n<\/table>\n<div style=\"text-align:center;\">\n<input  value=\"Mostrar a Planilha\" style=\"cursor:pointer; padding: 0px; width: 180px; height: 40px; background-color:#CDBA96; font-size: 20px; font-family: calibri, sans-serif; font-weight: bold; color: #FFFAFA;\" onclick=    \"if(this.parentNode.getElementsByTagName('div')[0].style.display != ''){this.parentNode.getElementsByTagName('div')[0].style.display = '';this.value = 'Ocultar a Planilha';} else{this.parentNode.getElementsByTagName('div')[0].style.display = 'none'; this.value = 'Mostrar a Planilha';}\"    type=\"button\" \/>    <\/p>\n<div style=\"display: none;\">\n<div style=\"border: 1px dotted #8B5A2B; padding: 10px; width: 85%; margin-left: auto; margin-right: auto;\">\n<p style=\"text-align: justify\"><span style=\"font-family: verdana, Arial, Helvetica, sans-serif; font-size: 14px; text-align: justify; color: #616161; line-height: 25px;\">1) Abra a planilha e aguarde o arquivo carregar.<br \/>\n2) Podemos observar um tri\u00e2ngulo <strong>ABC<\/strong> e as medidas de seus \u00e2ngulos internos. Voc\u00ea pode movimentar os pontos <strong>A<\/strong> e <strong>B<\/strong> para modificar a forma do tri\u00e2ngulo.<br \/>\n3) Movimente os pontos <strong>A<\/strong>, <strong>B<\/strong> e observe v\u00e1rios exemplos do resultado obtido.<br \/>\n4) \u00c9 importante que voc\u00ea saiba que o GeoGebra fornece valores aproximados para as medidas apresentadas.<\/span><\/p>\n<p style=\"margin:20px\">\n<p>\tPara abrir a planilha din\u00e2mica, clique <a href=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/yfzpag4t\/width\/785\/height\/583\/border\/ffffff\/smb\/false\/stb\/false\/stbh\/false\/ai\/false\/asb\/false\/sri\/false\/rc\/false\/ld\/false\/sdz\/false\/ctl\/false\" target=\"ap2\"><span style=\"color: #8B5A2B;font-size: 16px;\"><strong>AQUI<\/strong><\/span><\/a><br \/>\n<iframe  name=\"ap2\"  width=\"790\" height=\"600\" style=\"border: 4px solid #8B5A2B;\"> <\/iframe><span style=\"font-size: 14px;\"><br \/>\n\tOBMEP_ srdg, criado com o <a href=\"http:\/\/www.geogebra.org\/\" target=\"_blank\">GeoGebra<\/a><\/span><br \/>\n\t<span style=\"font-family: Georgia, Times, 'Times New Roman', serif; font-size: 14px; text-align: justify; color: #8B5A2B; line-height: 15px;\">Observamos que a planilha ajuda na visualiza\u00e7\u00e3o do resultado; mas, matematicamente, n\u00e3o substitui sua demonstra\u00e7\u00e3o.<\/span>\n<\/div>\n<\/div>\n<\/div>\n<p style=\"margin:30px\">\n<hr style=\"height:2px; width:95%;background-color:#8B5A2B; margin-top:8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:3px; width:98%;background-color:#8B5A2B; margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<p style=\"margin:30px \">\n<table style=\" height:auto; margin-left: auto; margin-right: auto; width:540px;\">\n<tr class=\"bf\">\n<td style=\"border: 1px solid  #ffffff;\">\n<p style=\"padding-right: 300px; text-align: justify; padding: 15px; border-style: dotted; border-color :#1C1C1C; border-width :thin; width:420px;background-color: #CDBA96;\"><span style=\"color: #000000; font-family: Georgia, Times, 'Times New Roman', serif; font-size: 16px;\">Legal, agora sabemos que  a soma, em graus, das medidas dos \u00e2ngulos internos de um tri\u00e2ngulo \u00e9 [tex] 180^\\circ[\/tex]!<\/span><\/p>\n<p><\/td>\n<td style=\"border: 1px solid #ffffff\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/02\/carinha1.jpg\" alt=\"\" width=\"85\" height=\"80\" class=\"aligncenter size-full wp-image-3063\" \/><\/td>\n<\/tr>\n<\/table>\n<table style=\" height:auto; margin-left: auto; margin-right: auto; width:640px;\">\n<tr>\n<td style=\"border: 1px solid #ffffff\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1001 alignright\" style=\"border: 0px;\" alt=\"\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/01\/menino.jpg\" width=\"95\" height=\"115\" \/><\/td>\n<td  style=\"border: 1px solid  #ffffff\">\n<p style=\"text-align: justify; padding: 15px; border-style: dotted; border-color :#1C1C1C; border-width :thin; width:510px; background-color: #CDBA96;\"><span style=\"color: #1C1C1C; font-family: Georgia, Times, 'Times New Roman', serif; font-size: 16px;\"> Para completar o nosso estudo, s\u00f3 falta justificarmos devidamente os fatos utilizados.<br \/>\nTente fazer isso na <a href=\"http:\/\/clubes.obmep.org.br\/blog\/?p=15512\" title=\"Clique aqui para visitar a Sala!\" target=\"_blank\"><span style=\"color: #FFFAFA; font-family: verdana, Arial, Helvetica, sans-serif; font-size: 14px;\"><strong> pr\u00f3xima Sala.<\/strong><\/span><\/a><br \/>\n\t<strong>Bons estudos!<\/strong><\/span><\/p>\n<\/td>\n<\/tr>\n<\/table>\n<hr style=\"height:3px; width:100%;background-color:#8B5A2B; margin-top: 6px; margin-bottom: 6px; border: 0 none\"\/>\n<hr style=\"height:2px; width:100%;background-color:#8B5A2B; margin-top: 6px; margin-bottom: 6px; border: 0 none\"\/>\n<p style=\"text-align: right;\"><span style=\"color: #8B5A2B;\"><strong>Equipe COM &#8211; OBMEP<\/strong><\/span><\/p>\n<\/div>\n<p style=\"font-size: 16px;line-height: 30px;text-align: right; color: #8B5A2B;\">Abril de 2014.<\/p>\n<p style=\"margin:20px\">\n<table style=\" height:auto; margin-left: auto; margin-right: auto;637px;\">\n<tr>\n<td style=\"border: 1px solid #ffffff\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1001 alignright\" style=\"border: 0px;\" alt=\"\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/01\/menino.jpg\" width=\"95\" height=\"115\" \/><\/td>\n<td  style=\"border: 1px solid  #ffffff\">\n<p style=\"text-align: justify; border-style: dotted; border-color: #8B5A2B; border-width: thin; width: 500px; background-color: #f5f3f3; padding: 15px;\"><span style=\"color: #1C1C1C; font-family: calibri, sans-serif; font-size: 14px;\">Se for conveniente, voc\u00ea pode utilizar a primeira planilha din\u00e2mica <em>off-line<\/em>. Para isso, copie o arquivo abaixo e abra-o no GeoGebra do seu computador ou tablet.<br \/>\nMas n\u00e3o se esque\u00e7a de visitar <a href=\"https:\/\/www.geogebra.org\/download\" title=\"site do GeoGebra\" target=\"_blank\"><span style=\"color: #a20000; font-family: verdana, Arial, Helvetica, sans-serif; font-size: 12px;\"><strong>este site<\/strong><\/span><\/a> e fazer a instala\u00e7\u00e3o da vers\u00e3o do <em>GeoGebra <\/em>adequada ao dispositivo utilizado.<\/span><\/p>\n<p><\/td>\n<\/tr>\n<\/table>\n<div style=\" float:right;  width: 120px;\">\n<p style=\"text-align: center; border-style: solid; border-color :#a20000; border-width :thin; width:90px;  height:40px;  padding: 5px; background-color: #f5f3f3;\">\n<a href=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2018\/08\/angext_02.ggb\"  title=\"Arquivo .ggb\"  download=\"angulos-internos.ggb\"><span style=\"color: #a20000; font-family: Georgia, Times, 'Times New Roman', serif;  font-size: 16px;\"><strong>Arquivo <\/strong><\/span><\/a>\n <\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Soma dos \u00e2ngulos internos de um tri\u00e2ngulo Qual \u00e9 a soma das medidas dos \u00e2ngulos internos de um dado tri\u00e2ngulo? Voc\u00ea n\u00e3o sabe? N\u00e3o faz mal, vamos calcul\u00e1-la juntos. Se necess\u00e1rio, veja algumas defini\u00e7\u00f5es AQUI, para que voc\u00ea n\u00e3o fique com d\u00favidas&#8230;. (1) Trace uma reta r passando por um dos v\u00e9rtices do tri\u00e2ngulo e &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/brincando-com-geometria-soma-dos-angulos-internos-de-um-triangulo\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-6832","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/6832","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=6832"}],"version-history":[{"count":131,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/6832\/revisions"}],"predecessor-version":[{"id":223558,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/6832\/revisions\/223558"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=6832"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}