{"id":24320,"date":"2023-01-08T20:50:59","date_gmt":"2023-01-08T20:50:59","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24320"},"modified":"2023-01-17T23:44:03","modified_gmt":"2023-01-17T23:44:03","slug":"cinco-triangulos-equilateros-iguais","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24320","title":{"rendered":"Cinco tri\u00e2ngulos equil\u00e1teros iguais"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24320' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24320' class='GTTabs_curr'><a  id=\"24320_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24320' ><a  id=\"24320_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_24320'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>A figura abaixo \u00e9 composta por tri\u00e2ngulos equil\u00e1teros iguais.<br \/>Tem-se ainda que o ponto E \u00e9 o ponto m\u00e9dio de [AB] e os pontos A, B, F, G, H e I est\u00e3o alinhados.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"24322\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=24322\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-4.png\" data-orig-size=\"480,298\" 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_Pag115-4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-4.png\" class=\"aligncenter wp-image-24322\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-4-300x186.png\" alt=\"\" width=\"400\" height=\"248\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-4-300x186.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-4.png 480w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a><\/p>\n<ol>\n<li>Existe uma reflex\u00e3o deslizante que transforma o tri\u00e2ngulo [ABC] no tri\u00e2ngulo [DEF].<br \/>Identifica o eixo e o vetor associados a uma tal isometria.<\/li>\n<li>Identifica uma reflex\u00e3o deslizante que transforma o tri\u00e2ngulo de lado [AB] no tri\u00e2ngulo de lado [FH].<\/li>\n<li>Identifica o vetor que determina uma transla\u00e7\u00e3o que transforma o tri\u00e2ngulo de lado [AB] no tri\u00e2ngulo de lado [GI].<\/li>\n<li>Identificas algum eixo de simetria nesta figura? Justifica.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_24320' onClick='GTTabs_show(1,24320)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24320'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>A figura abaixo \u00e9 composta por tri\u00e2ngulos equil\u00e1teros iguais.<br \/>Tem-se ainda que o ponto E \u00e9 o ponto m\u00e9dio de [AB] e os pontos A, B, F, G, H e I est\u00e3o alinhados.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"24322\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=24322\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-4.png\" data-orig-size=\"480,298\" 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_Pag115-4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-4.png\" class=\"aligncenter wp-image-24322\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-4-300x186.png\" alt=\"\" width=\"400\" height=\"248\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-4-300x186.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-4.png 480w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a><\/p>\n<ol>\n<li>Na reflex\u00e3o deslizante que transforma o tri\u00e2ngulo [ABC] no tri\u00e2ngulo [DEF], o eixo de reflex\u00e3o e o vetor associados a esta isometria s\u00e3o: AI e \\(\\overrightarrow {AE} \\).<\/li>\n<li>Numa reflex\u00e3o deslizante que transforma o tri\u00e2ngulo de lado [AB] no tri\u00e2ngulo de lado [FH],\u00a0o eixo de reflex\u00e3o e o vetor associados s\u00e3o: AI e \\(\\overrightarrow {AF} \\).<\/li>\n<li>O vetor \\(\\overrightarrow {AG} \\) determina uma transla\u00e7\u00e3o que transforma o tri\u00e2ngulo de lado [AB] no tri\u00e2ngulo de lado [GI].<\/li>\n<li>Sim, identifico um eixo de simetria nesta figura: a reta perpendicular \u00e0 reta AI e que cont\u00e9m o ponto F.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_24320' onClick='GTTabs_show(0,24320)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A figura abaixo \u00e9 composta por tri\u00e2ngulos equil\u00e1teros iguais.Tem-se ainda que o ponto E \u00e9 o ponto m\u00e9dio de [AB] e os pontos A, B, F, G, H e I est\u00e3o&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":24323,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,685],"tags":[424,67,691,381,688],"series":[],"class_list":["post-24320","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-reflexao-deslizante","tag-translacao","tag-vetores"],"views":301,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-4_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24320","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=24320"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24320\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/24323"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24320"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24320"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24320"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24320"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}