{"id":23969,"date":"2022-12-29T01:23:42","date_gmt":"2022-12-29T01:23:42","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=23969"},"modified":"2023-01-17T23:29:00","modified_gmt":"2023-01-17T23:29:00","slug":"os-triangulos-sao-todos-iguais-e-equilateros","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=23969","title":{"rendered":"Os tri\u00e2ngulos s\u00e3o todos iguais e equil\u00e1teros"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_23969' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_23969' class='GTTabs_curr'><a  id=\"23969_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_23969' ><a  id=\"23969_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_23969'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Na figura, os tri\u00e2ngulos numerados s\u00e3o todos iguais e equil\u00e1teros.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23970\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23970\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-2.png\" data-orig-size=\"344,272\" 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_Pag102-2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-2.png\" class=\"aligncenter wp-image-23970 size-full\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-2.png\" alt=\"\" width=\"344\" height=\"272\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-2.png 344w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-2-300x237.png 300w\" sizes=\"auto, (max-width: 344px) 100vw, 344px\" \/><\/p>\n<ol>\n<li>Caracteriza:<br \/>a) uma rota\u00e7\u00e3o, uma transla\u00e7\u00e3o e uma reflex\u00e3o axial que transformem o tri\u00e2ngulo 4 no tri\u00e2ngulo 6;<br \/>b) duas isometrias diferentes que transformem o tri\u00e2ngulo 9 no tri\u00e2ngulo 8.<\/li>\n<li>Relaciona com \\({\\vec u}\\) e \\({\\vec v}\\) o vetor da transla\u00e7\u00e3o que transforma:<br \/>a) o tri\u00e2ngulo 9 no tri\u00e2ngulo 18;<br \/>b) o tri\u00e2ngulo 3 no tri\u00e2ngulo 16;<br \/>c) o tri\u00e2ngulo 16 no tri\u00e2ngulo 1.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_23969' onClick='GTTabs_show(1,23969)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_23969'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Na figura, os tri\u00e2ngulos numerados s\u00e3o todos iguais e equil\u00e1teros.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-2_Pontos.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23972\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23972\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-2_Pontos.png\" data-orig-size=\"344,272\" 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_Pag102-2_Pontos\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-2_Pontos.png\" class=\"aligncenter wp-image-23972 size-full\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-2_Pontos.png\" alt=\"\" width=\"344\" height=\"272\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-2_Pontos.png 344w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-2_Pontos-300x237.png 300w\" sizes=\"auto, (max-width: 344px) 100vw, 344px\" \/><\/a><\/p>\n<ol>\n<li>Caracteriza:<br \/>a) uma rota\u00e7\u00e3o, uma transla\u00e7\u00e3o e uma reflex\u00e3o axial que transformem o tri\u00e2ngulo 4 no tri\u00e2ngulo 6;<br \/><span style=\"color: #0000ff;\">\u00a0 \u00a0 \u2022 \\({R_{A,240^\\circ }}\\left( {t4} \\right) = t6\\)<\/span><br \/><span style=\"color: #0000ff;\">\u00a0 \u00a0 \u2022 \\({T_{\\vec v}}\\left( {t4} \\right) = t6\\)<\/span><br \/><span style=\"color: #0000ff;\">\u00a0 \u00a0 \u2022 \\({S_{AC}}\\left( {t4} \\right) = t6\\)<\/span><br \/>b) duas isometrias diferentes que transformem o tri\u00e2ngulo 9 no tri\u00e2ngulo 8.<br \/><span style=\"color: #0000ff;\">\u00a0 \u00a0 \u2022 \\({R_{B, &#8211; 60^\\circ }}\\left( {t9} \\right) = t8\\)<\/span><br \/><span style=\"color: #0000ff;\">\u00a0 \u00a0 \u2022 \\({S_{AB}}\\left( {t9} \\right) = t8\\)<\/span><\/li>\n<li>Relaciona com \\({\\vec u}\\) e \\({\\vec v}\\) o vetor da transla\u00e7\u00e3o que transforma:<br \/>a) o tri\u00e2ngulo 9 no tri\u00e2ngulo 18;<br \/><span style=\"color: #0000ff;\">\u00a0 \u00a0 \u2022 \\({T_{\\vec u + \\vec v}}\\left( {t9} \\right) = t18\\)<\/span><br \/>b) o tri\u00e2ngulo 3 no tri\u00e2ngulo 16;<br \/><span style=\"color: #0000ff;\">\u00a0 \u00a0 \u2022 \\({T_{2\\vec u}}\\left( {t3} \\right) = t16\\)<\/span><br \/>c) o tri\u00e2ngulo 16 no tri\u00e2ngulo 1.<br \/><span style=\"color: #0000ff;\">\u00a0 \u00a0 \u2022 \\({T_{ &#8211; 2\\vec u &#8211; \\vec v}}\\left( {t16} \\right) = t1\\)<\/span><\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23969' onClick='GTTabs_show(0,23969)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na figura, os tri\u00e2ngulos numerados s\u00e3o todos iguais e equil\u00e1teros. Caracteriza:a) uma rota\u00e7\u00e3o, uma transla\u00e7\u00e3o e uma reflex\u00e3o axial que transformem o tri\u00e2ngulo 4 no tri\u00e2ngulo 6;b) duas isometrias diferentes que&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":23971,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,685],"tags":[424,67,686,690,382,381,688],"series":[],"class_list":["post-23969","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-reflexao-axial","tag-rotacao","tag-translacao","tag-vetores"],"views":102,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag102-2_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23969","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=23969"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23969\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/23971"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23969"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23969"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23969"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=23969"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}