{"id":15717,"date":"2014-03-03T17:19:22","date_gmt":"2014-03-03T20:19:22","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=15717"},"modified":"2023-01-26T00:48:48","modified_gmt":"2023-01-26T03:48:48","slug":"soma-dos-angulos-internos-de-um-triangulo-conferindo","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/brincando-com-geometria-soma-dos-angulos-internos-de-um-triangulo\/soma-dos-angulos-internos-de-um-triangulo-conferindo\/","title":{"rendered":"Soma dos \u00e2ngulos internos de um tri\u00e2ngulo &#8211; conferindo . . ."},"content":{"rendered":"<p style=\"margin:20px \">\n<div style=\"border: 8px double #8B5A2B; padding: 10px;padding-left: 20px; padding-right: 20px; text-align:justify\">\n<p style=\"text-align: center;  margin:20px\"><span style=\"color: #8B5A2B; font-family: verdana, Arial, Helvetica, sans-serif; font-size: 26px;\"><strong>Soma dos \u00e2ngulos internos de um tri\u00e2ngulo &#8211; conferindo . . .<\/strong><\/span><\/p>\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: 30px; border: 0 none\"\/>\n<table style=\" height:auto; margin-left: auto; margin-right: auto; width:637px;\">\n<tr class=\"bf\">\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 :#c1c1c1; border-width :thin; width:500px;background-color: #CDBA96;\"><span style=\"color: #000000; font-family: Georgia, Times, 'Times New Roman', serif; font-size: 16px;\">Para um melhor entendimento sobre o assunto e para conferir suas respostas, assista ao v\u00eddeo abaixo.<\/span><\/p>\n<p><\/td>\n<\/tr>\n<\/table>\n<p style=\"margin:30px \">\n<div style=\"border: 3px solid #8B5A2B; padding: 5px;padding-left: 20px; padding-right: 20px;\">\n<p style=\"text-align: center;   padding-right: 15px;line-height:25px;margin:10px\"><span style=\"color: #8B5A2B; font-family: verdana, Arial, Helvetica, sans-serif; font-size: 24px;\"><strong>Um v\u00eddeo<\/strong><\/span><\/p>\n<hr style=\"height:2px;background-color:#8B5A2B; margin-top: 8px; margin-bottom: 8px;  border: 0 none\"\/>\n<hr style=\"height:1px; width:80%;background-color:#8B5A2B; margin-top: 8px; margin-bottom: 40px;  border: 0 none\"\/>\n<p style=\"text-align:center;\">\n<iframe loading=\"lazy\" width=\"640\" height=\"360\" src=\"\/\/www.youtube.com\/embed\/Gr54jtaDZWQ?rel=0\"  allowfullscreen><\/iframe><br \/>\n<span style=\"font-family: calibri, sans-serif; font-size: 16px;\">\t<strong> Soma dos \u00e2ngulos internos de um tri\u00e2ngulo.<\/strong><br \/>\nProfessor Marcos Paulo Ferreira de Ara\u00fajo.<\/span><\/p>\n<p style=\"margin:10px \">\n<\/div>\n<p style=\"margin:20px \">\n<table style=\" height:auto; margin-left: auto; margin-right: auto; width:370px;\">\n<tr class=\"bf\">\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: 10px; border-style: dotted; border-color :#c1c1c1; border-width:thin; width:250px; background-color: #CDBA96;\"><span style=\"color: #000000; font-family: Georgia, Times, 'Times New Roman', serif; font-size: 16px;\">Dois applets para finalizar.<\/span ><\/p>\n<p><\/td>\n<\/tr>\n<\/table>\n<p style=\"margin:20px \">\n<div style=\"border: 3px solid #8B5A2B; padding: 5px;padding-left: 20px; padding-right: 20px;\">\n<p style=\"text-align: center;   padding-right: 15px;line-height:25px;margin:10px\"><span style=\"color: #8B5A2B; font-family: verdana, Arial, Helvetica, sans-serif; font-size: 24px;\"><strong>Para relaxar . . . <\/strong><\/span><\/p>\n<hr style=\"height:2px;background-color:#8B5A2B;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:1px; width:80%;background-color:#8B5A2B;  margin-top: 8px; margin-bottom: 50px; border: 0 none\"\/>\n<div style=\"text-align:center;\">\n<input value=\"Mostrar o Applet\" 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 o applet';} else{this.parentNode.getElementsByTagName('div')[0].style.display = 'none'; this.value = 'Mostrar o Applet';}\"    type=\"button\" \/>    <\/p>\n<div style=\"display: none;\">\n<div style=\"border: 1px dotted #8B5A2B; padding: 10px; width: 90%; margin-left: auto; margin-right: auto;\">\n<p style=\"text-align: justify\"><span style=\"font-family: verdana, Arial, Helvetica, sans-serif; font-size: 13px; text-align: justify; color: #616161; line-height: 25px;\">1) Aguarde o applet carregar.<br \/>\n2) Na planilha, fixamos uma circunfer\u00eancia, um tri\u00e2ngulo ABC e destacamos tr\u00eas regi\u00f5es definidas pelos \u00e2ngulos externos desse tri\u00e2ngulo (uma por v\u00e9rtice).<br \/>\n3) Com o aux\u00edlio de qualquer bot\u00e3o do mouse pressionado, arraste as regi\u00f5es coloridas e obtenha a ilustra\u00e7\u00e3o de um dos resultados discutidos nesta Sala de Estudo. (Se voc\u00ea estiver utilizando um celular ou um tablet, toque levemente em cada regi\u00e3o e movimente-a.)<br \/>\n4) Se precisar voltar para a visualiza\u00e7\u00e3o inicial, clique nas setinhas circulares que aparecem no canto superior direito do aplicativo.<\/span><\/p>\n<p style=\"margin:20px\">\n<p><iframe loading=\"lazy\" scrolling=\"no\" title=\"Brincando com geometria 6\" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/ZPs5mPkf\/width\/735\/height\/650\/border\/ffffff\/sfsb\/false\/smb\/false\/stb\/false\/stbh\/false\/ai\/false\/asb\/false\/sri\/true\/rc\/false\/ld\/false\/sdz\/false\/ctl\/false\" width=\"735px\" height=\"650px\" style=\"border: 1px solid #8B5A2B;\"> <\/iframe><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: 12px; 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<p style=\"margin:10px \">\n<\/div>\n<\/div>\n<p style=\"margin:40px \">\n<\/div>\n<p style=\"margin:50px \">\n<div style=\"border: 3px solid #8B5A2B; padding: 5px;padding-left: 20px; padding-right: 20px; font-size: 14px;font-family: verdana, Arial, Helvetica, sans-serif; \">\n<p style=\"text-align: center;   padding-right: 15px;line-height:25px;margin:10px\"><span style=\"color: #8B5A2B; font-family: verdana, Arial, Helvetica, sans-serif; font-size: 24px;\"><strong>Passando a limpo duas propriedades<\/strong><\/span><\/p>\n<hr style=\"height:2px;background-color:#8B5A2B;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:1px; width:80%;background-color:#8B5A2B;  margin-top: 8px; margin-bottom: 20px; border: 0 none\"\/>\nCom o pr\u00f3ximo applet, podemos obter v\u00e1rios tri\u00e2ngulos e visualizar duas propriedades importantes que apareceram nas nossas discuss\u00f5es e foram demonstradas no v\u00eddeo acima:<\/p>\n<ul>\n<li>A soma das medidas dos \u00e2ngulos internos de um tri\u00e2ngulo \u00e9 [tex] 180^\\circ[\/tex].<\/li>\n<li>A soma das medidas dos \u00e2ngulos externos de um tri\u00e2ngulo (um por v\u00e9rtice) \u00e9 [tex] 360^\\circ[\/tex].<\/li>\n<\/ul>\n<div style=\"text-align:center;\">\n<input value=\"Mostrar o Applet\" 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 o applet';} else{this.parentNode.getElementsByTagName('div')[0].style.display = 'none'; this.value = 'Mostrar o Applet';}\"    type=\"button\" \/>    <\/p>\n<div style=\"display: none;\">\n<div style=\"border: 1px dotted #8B5A2B; padding: 10px; width: 90%; margin-left: auto; margin-right: auto;\">\n<p style=\"text-align: justify\"><span style=\"font-family: verdana, Arial, Helvetica, sans-serif; font-size: 13px; text-align: justify; color: #616161; line-height: 25px;\"> 1) Aguarde o applet carregar.<br \/>\n2) Na planilha, voc\u00ea visualizar\u00e1 um tri\u00e2ngulo [tex]ABC[\/tex], as medidas, em graus, de seus \u00e2ngulos internos e externos e as somas dessas medidas.  Voc\u00ea pode movimentar os v\u00e9rtices do tri\u00e2ngulo para modificar a sua forma, o tamanho dos seus lados e, consequentemente, as medidas dos seus \u00e2ngulos internos e externos. A cada movimento de um dos v\u00e9rtices, o aplicativo atualiza imediatamente a soma das medidas dos \u00e2ngulos internos e a soma das medidas dos \u00e2ngulos externos do tri\u00e2ngulo.<br \/>\n3) Para movimentar qualquer v\u00e9rtice, clique sobre ele com qualquer bot\u00e3o do mouse, mantenha o bot\u00e3o pressionado e fa\u00e7a o movimento. (Se voc\u00ea estiver utilizando um celular ou um tablet, toque levemente no ponto e movimente-o.)<br \/>\n4) Duas observa\u00e7\u00f5es importantes:<br \/>\n&#8211; O GeoGebra fornece valores aproximados para as medidas apresentadas.<br \/>\n&#8211; O GeoGebra utiliza ponto e n\u00e3o v\u00edrgula como separador decimal.<\/span><\/p>\n<p><iframe loading=\"lazy\" scrolling=\"no\" title=\"\u00c2ngulos em um  tri\u00e2ngulo\" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/etsedpb9\/width\/713\/height\/548\/border\/ffffff\/sfsb\/false\/smb\/false\/stb\/false\/stbh\/false\/ai\/false\/asb\/false\/sri\/false\/rc\/false\/ld\/false\/sdz\/false\/ctl\/false\" width=\"713px\" height=\"550px\"  style=\"border:1px solid #8B5A2B;\"> <\/iframe><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: 12px; 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<p style=\"margin:10px \">\n<\/div>\n<\/div>\n<p style=\"margin:40px \">\n<\/div>\n<p style=\"margin:30px \">\n<p style=\"margin:30px \">\n<table style=\" height:auto; margin-left: auto; margin-right: auto; width:280px;\">\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:150px;background-color: #CDBA96;\"><span style=\"color: #000000; font-family: Georgia, Times, 'Times New Roman', serif; font-size: 16px;\"><strong>F&nbsp;e&nbsp;c&nbsp;h&nbsp;o&nbsp;u&nbsp;.&nbsp;.&nbsp;.<\/strong><\/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\/carinha2.jpg\" style=\"border: 0px;\" alt=\"carinha2\" width=\"80\" height=\"80\" class=\"alignleft size-full wp-image-3064\" \/><\/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=\"margin:10px \">\n<p style=\"text-align: right;\"><a href=\"http:\/\/clubes.obmep.org.br\/blog\/?p=6832\" title=\"Voltar\" target=\"_blank\"><span style=\"color: #8B5A2B;\"><strong>Voltar para a Sala de Estudos sobre a soma dos \u00e2ngulos internos de um tri\u00e2ngulo <\/strong><\/span><\/a><\/p>\n<p style=\"text-align: right;\"><a href=\"http:\/\/clubes.obmep.org.br\/blog\/?p=15512\" title=\"Voltar para os problemas\" target=\"_blank\"><span style=\"color: #8B5A2B;\"><strong>Voltar para a Sala de Estudos com os problemas sobre a soma dos \u00e2ngulos internos de um tri\u00e2ngulo. <\/strong><\/span><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Soma dos \u00e2ngulos internos de um tri\u00e2ngulo &#8211; conferindo . . . Para um melhor entendimento sobre o assunto e para conferir suas respostas, assista ao v\u00eddeo abaixo. Um v\u00eddeo Soma dos \u00e2ngulos internos de um tri\u00e2ngulo. Professor Marcos Paulo Ferreira de Ara\u00fajo. Dois applets para finalizar. Para relaxar . . . 1) Aguarde o &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\/soma-dos-angulos-internos-de-um-triangulo-conferindo\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":6832,"menu_order":1,"comment_status":"open","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-15717","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/15717","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=15717"}],"version-history":[{"count":42,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/15717\/revisions"}],"predecessor-version":[{"id":16455,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/15717\/revisions\/16455"}],"up":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/6832"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=15717"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}