{"id":23133,"date":"2022-11-18T18:31:10","date_gmt":"2022-11-18T18:31:10","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=23133"},"modified":"2023-06-12T00:14:41","modified_gmt":"2023-06-11T23:14:41","slug":"em-busca-do-teorema-de-pitagoras","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=23133","title":{"rendered":"Em busca do Teorema de Pit\u00e1goras"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_23133' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_23133' class='GTTabs_curr'><a  id=\"23133_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_23133' ><a  id=\"23133_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_23133'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Observa as figuras compostas por tri\u00e2ngulos ret\u00e2ngulos e pelos quadrados constru\u00eddos sobre a hipotenusa e sobre cada um dos catetos.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23136\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23136\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4.png\" data-orig-size=\"1120,368\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&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;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag051-T4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4-1024x336.png\" class=\"aligncenter wp-image-23136\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4-1024x336.png\" alt=\"\" width=\"980\" height=\"322\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4-1024x336.png 1024w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4-300x99.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4-768x252.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4.png 1120w\" sizes=\"auto, (max-width: 980px) 100vw, 980px\" \/><\/a><\/p>\n<ol>\n<li>Completa a tabela seguinte.<br \/><br \/>\n<table class=\"tabela-2\" style=\"border-collapse: collapse none; width: 100%;\">\n<thead>\n<tr>\n<td style=\"width: 25%; background-color: #a60c0c;\"><span style=\"color: #ffffff;\">Figura<\/span><\/td>\n<td style=\"width: 25%; background-color: #a60c0c;\"><span style=\"color: #ffffff;\">\u00c1rea do quadrado assente sobre um dos catetos<\/span><\/td>\n<td style=\"width: 25%; background-color: #a60c0c;\"><span style=\"color: #ffffff;\">\u00c1rea do quadrado assente sobre o outro cateto<\/span><\/td>\n<td style=\"width: 25%; background-color: #a60c0c;\"><span style=\"color: #ffffff;\">\u00c1rea do quadrado assente sobre a hipotenusa<\/span><\/td>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"width: 25%; background-color: #e3a832;\"><strong><span style=\"color: #ffffff;\">A<\/span><\/strong><\/td>\n<td style=\"width: 25%; background-color: #f2df99;\">\u00a0<\/td>\n<td style=\"width: 25%; background-color: #f2df99;\">\u00a0<\/td>\n<td style=\"width: 25%; background-color: #f2df99;\">\u00a0<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 25%; background-color: #e3a832;\"><strong><span style=\"color: #ffffff;\">B<\/span><\/strong><\/td>\n<td style=\"width: 25%; background-color: #f2df99;\">\u00a0<\/td>\n<td style=\"width: 25%; background-color: #f2df99;\">\u00a0<\/td>\n<td style=\"width: 25%; background-color: #f2df99;\">\u00a0<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 25%; background-color: #e3a832;\"><strong><span style=\"color: #ffffff;\">C<\/span><\/strong><\/td>\n<td style=\"width: 25%; background-color: #f2df99;\">\u00a0<\/td>\n<td style=\"width: 25%; background-color: #f2df99;\">\u00a0<\/td>\n<td style=\"width: 25%; background-color: #f2df99;\">\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>Qual \u00e9 a rela\u00e7\u00e3o entre as \u00e1reas dos quadrados de cada uma das figuras?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_23133' onClick='GTTabs_show(1,23133)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_23133'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>As figuras s\u00e3o compostas por tri\u00e2ngulos ret\u00e2ngulos e por quadrados constru\u00eddos sobre a hipotenusa e sobre cada um dos catetos.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23136\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23136\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4.png\" data-orig-size=\"1120,368\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&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;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag051-T4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4-1024x336.png\" class=\"aligncenter wp-image-23136\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4-1024x336.png\" alt=\"\" width=\"980\" height=\"322\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4-1024x336.png 1024w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4-300x99.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4-768x252.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4.png 1120w\" sizes=\"auto, (max-width: 980px) 100vw, 980px\" \/><\/a><\/p>\n<ol>\n<li>Completando a tabela:<br \/><br \/>\n<table class=\"tabela-2\" style=\"border-collapse: collapse none; width: 100%;\">\n<thead>\n<tr>\n<td style=\"width: 25%; background-color: #a60c0c;\"><span style=\"color: #ffffff;\">Figura<\/span><\/td>\n<td style=\"width: 25%; background-color: #a60c0c;\"><span style=\"color: #ffffff;\">\u00c1rea do quadrado assente sobre um dos catetos<\/span><\/td>\n<td style=\"width: 25%; background-color: #a60c0c;\"><span style=\"color: #ffffff;\">\u00c1rea do quadrado assente sobre o outro cateto<\/span><\/td>\n<td style=\"width: 25%; background-color: #a60c0c;\"><span style=\"color: #ffffff;\">\u00c1rea do quadrado assente sobre a hipotenusa<\/span><\/td>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"width: 25%; background-color: #e3a832;\"><strong><span style=\"color: #ffffff;\">A<\/span><\/strong><\/td>\n<td style=\"width: 25%; background-color: #f2df99;\">\\[{1^2} = 1\\]<\/td>\n<td style=\"width: 25%; background-color: #f2df99;\">\\[{2^2} = 4\\]<\/td>\n<td style=\"width: 25%; background-color: #f2df99;\">\\[{3^2} &#8211; 4 \\times \\frac{{1 \\times 2}}{2} = 5\\]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 25%; background-color: #e3a832;\"><strong><span style=\"color: #ffffff;\">B<\/span><\/strong><\/td>\n<td style=\"width: 25%; background-color: #f2df99;\">\\[{2^2} = 4\\]<\/td>\n<td style=\"width: 25%; background-color: #f2df99;\">\\[{2^2} = 4\\]<\/td>\n<td style=\"width: 25%; background-color: #f2df99;\">\\[{4^2} &#8211; 4 \\times \\frac{{2 \\times 2}}{2} = 8\\]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 25%; background-color: #e3a832;\"><strong><span style=\"color: #ffffff;\">C<\/span><\/strong><\/td>\n<td style=\"width: 25%; background-color: #f2df99;\">\\[{1^2} = 1\\]<\/td>\n<td style=\"width: 25%; background-color: #f2df99;\">\\[{3^2} = 9\\]<\/td>\n<td style=\"width: 25%; background-color: #f2df99;\">\\[{4^2} &#8211; 4 \\times \\frac{{1 \\times 3}}{2} = 10\\]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>A rela\u00e7\u00e3o entre as \u00e1reas dos quadrados de cada uma das figuras \u00e9 a seguinte:<br \/><strong>A soma das \u00e1reas dos quadrados assentes sobre os catetos \u00e9 igual \u00e0 \u00e1rea do quadrado assente sobre a hipotenusa<\/strong>.<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<h6>Explica\u00e7\u00e3o do c\u00e1lculo da \u00e1rea do quadrado sobre a hipotenusa<\/h6>\n<p>\\[{A_{{\\rm{Verde}}}} = {4^2} &#8211; {A_{{\\rm{Amarela}}}} = {4^2} &#8211; 4 \\times \\frac{{2 \\times 2}}{2} = 16 &#8211; 8 = 8\\]<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4_Expl-Calculo.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23148\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23148\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4_Expl-Calculo.png\" data-orig-size=\"1120,368\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&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;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag051-T4_Expl-Calculo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4_Expl-Calculo-1024x336.png\" class=\"aligncenter wp-image-23148\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4_Expl-Calculo-300x99.png\" alt=\"\" width=\"980\" height=\"322\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4_Expl-Calculo-300x99.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4_Expl-Calculo-1024x336.png 1024w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4_Expl-Calculo-768x252.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4_Expl-Calculo.png 1120w\" sizes=\"auto, (max-width: 980px) 100vw, 980px\" \/><\/a><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23133' onClick='GTTabs_show(0,23133)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Observa as figuras compostas por tri\u00e2ngulos ret\u00e2ngulos e pelos quadrados constru\u00eddos sobre a hipotenusa e sobre cada um dos catetos. Completa a tabela seguinte. Figura \u00c1rea do quadrado assente sobre um&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":23138,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,682],"tags":[424,108,67,118],"series":[],"class_list":["post-23133","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-teorema-de-pitagoras","tag-8-o-ano","tag-area","tag-geometria","tag-teorema-de-pitagoras"],"views":263,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag051-T4_520x245_b.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23133","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=23133"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23133\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/23138"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23133"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23133"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23133"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=23133"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}