{"id":23991,"date":"2022-12-29T14:24:08","date_gmt":"2022-12-29T14:24:08","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=23991"},"modified":"2023-01-17T23:29:41","modified_gmt":"2023-01-17T23:29:41","slug":"dois-pares-de-triangulos","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=23991","title":{"rendered":"Tr\u00eas pares de tri\u00e2ngulos"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_23991' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_23991' class='GTTabs_curr'><a  id=\"23991_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_23991' ><a  id=\"23991_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_23991'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Haver\u00e1 alguma transla\u00e7\u00e3o que transforme o tri\u00e2ngulo I no tri\u00e2ngulo II?<br \/>Explica a tua resposta.<\/p>\n<table style=\"border-collapse: collapse;\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td style=\"text-align: left;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5a.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23993\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23993\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5a.png\" data-orig-size=\"584,210\" 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_Pag102-5a\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5a.png\" class=\"alignnone wp-image-23993\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5a-300x108.png\" alt=\"\" width=\"420\" height=\"151\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5a-300x108.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5a.png 584w\" sizes=\"auto, (max-width: 420px) 100vw, 420px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td>b)<\/td>\n<td style=\"text-align: left;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23994\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23994\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5b.png\" data-orig-size=\"584,280\" 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_Pag102-5b\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5b.png\" class=\"alignnone wp-image-23994\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5b-300x144.png\" alt=\"\" width=\"420\" height=\"201\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5b-300x144.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5b.png 584w\" sizes=\"auto, (max-width: 420px) 100vw, 420px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td>c)<\/td>\n<td style=\"text-align: left;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5c.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"24004\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=24004\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5c.png\" data-orig-size=\"584,238\" 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_Pag102-5c\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5c.png\" class=\"alignnone wp-image-24004\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5c-300x122.png\" alt=\"\" width=\"420\" height=\"171\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5c-300x122.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5c.png 584w\" sizes=\"auto, (max-width: 420px) 100vw, 420px\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_23991' onClick='GTTabs_show(1,23991)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_23991'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Haver\u00e1 alguma transla\u00e7\u00e3o que transforme o tri\u00e2ngulo I no tri\u00e2ngulo II?<br \/>Explica a tua resposta.<\/p>\n<table style=\"border-collapse: collapse;\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td style=\"width: 420px;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5a.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23993\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23993\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5a.png\" data-orig-size=\"584,210\" 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_Pag102-5a\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5a.png\" class=\"alignnone wp-image-23993\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5a-300x108.png\" alt=\"\" width=\"420\" height=\"151\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5a-300x108.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5a.png 584w\" sizes=\"auto, (max-width: 420px) 100vw, 420px\" \/><\/a><\/td>\n<td style=\"text-align: left; vertical-align: top;\">\n<p style=\"text-align: left;\"><span style=\"color: #0000ff;\">Tendo em considera\u00e7\u00e3o que, num tri\u00e2ngulo, a lados iguais se op\u00f5em \u00e2ngulos iguais, podemos concluir que os tri\u00e2ngulos s\u00e3o geometricamente iguais (crit\u00e9rio LAL).<\/span><br \/><span style=\"color: #0000ff;\">No pressuposto de serem paralelos os lados correspondentes dos dois tri\u00e2ngulos, conclui-se que o tri\u00e2ngulo II pode ser obtido a partir do tri\u00e2ngulo I pela transla\u00e7\u00e3o de vetor \\(\\overrightarrow {AD} \\).<\/span><\/p>\n<p>\u00a0<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>b)<\/td>\n<td style=\"text-align: left; width: 420px;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23994\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23994\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5b.png\" data-orig-size=\"584,280\" 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_Pag102-5b\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5b.png\" class=\"alignnone wp-image-23994\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5b-300x144.png\" alt=\"\" width=\"420\" height=\"201\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5b-300x144.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5b.png 584w\" sizes=\"auto, (max-width: 420px) 100vw, 420px\" \/><\/a><\/td>\n<td style=\"text-align: left; vertical-align: top;\"><span style=\"color: #0000ff;\">Ainda que os tri\u00e2ngulos sejam geometricamente iguais, os seus lados correspondents n\u00e3o s\u00e3o paralelos. Consequentemente, o tri\u00e2ngulo II n\u00e3o pode ser o transformado do tri\u00e2ngulo I por uma transla\u00e7\u00e3o, pois uma transla\u00e7\u00e3o preserva a dire\u00e7\u00e3o e sentido dos segmentos orientados e semirretas.<\/span><\/td>\n<\/tr>\n<tr>\n<td>c)<\/td>\n<td style=\"text-align: left; width: 420px;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5c.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"24004\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=24004\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5c.png\" data-orig-size=\"584,238\" 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_Pag102-5c\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5c.png\" class=\"alignnone wp-image-24004\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5c-300x122.png\" alt=\"\" width=\"420\" height=\"171\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5c-300x122.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5c.png 584w\" sizes=\"auto, (max-width: 420px) 100vw, 420px\" \/><\/a><\/td>\n<td style=\"text-align: left; vertical-align: top;\"><span style=\"color: #0000ff;\">Os tri\u00e2ngulos s\u00e3o semelhantes, mas n\u00e3o s\u00e3o geometricamente iguais. Consequentemente, o tri\u00e2ngulo II n\u00e3o pode ser o transformado do tri\u00e2ngulo I por uma transla\u00e7\u00e3o, pois uma transla\u00e7\u00e3o preserva o comprimento dos segmentos de reta.<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23991' onClick='GTTabs_show(0,23991)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Haver\u00e1 alguma transla\u00e7\u00e3o que transforme o tri\u00e2ngulo I no tri\u00e2ngulo II?Explica a tua resposta. a) b) c) Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":23995,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,685],"tags":[424,67,686,381,688],"series":[],"class_list":["post-23991","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-isometrias","tag-8-o-ano","tag-geometria","tag-isometria","tag-translacao","tag-vetores"],"views":194,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-5b_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23991","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=23991"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23991\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/23995"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23991"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23991"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23991"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=23991"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}