{"id":24135,"date":"2023-01-02T18:34:34","date_gmt":"2023-01-02T18:34:34","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24135"},"modified":"2023-01-17T23:37:07","modified_gmt":"2023-01-17T23:37:07","slug":"seis-triangulos-equilateros-geometricamente-iguais","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24135","title":{"rendered":"Seis tri\u00e2ngulos equil\u00e1teros geometricamente iguais"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24135' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24135' class='GTTabs_curr'><a  id=\"24135_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24135' ><a  id=\"24135_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_24135'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag108-6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"24136\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=24136\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag108-6.png\" data-orig-size=\"305,276\" 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_Pag108-6\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag108-6.png\" class=\"alignright wp-image-24136\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag108-6-300x271.png\" alt=\"\" width=\"270\" height=\"244\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag108-6-300x271.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag108-6.png 305w\" sizes=\"auto, (max-width: 270px) 100vw, 270px\" \/><\/a>Considera a figura em que est\u00e3o representados tri\u00e2ngulos equil\u00e1teros geometricamente iguais.<\/p>\n<ol>\n<li>Indica um vetor igual a \\(\\overrightarrow {GE} \\).<\/li>\n<li>Indica um vetor sim\u00e9trico de \\(\\overrightarrow {AF} \\).<\/li>\n<li>Determina:<br \/>a) \\(\\overrightarrow {HB} + \\overrightarrow {BF} \\)<br \/>b) \\(\\overrightarrow {AF} + \\overrightarrow {BE} \\)<br \/>c) \\(\\overrightarrow {DG} + \\overrightarrow {BC} \\)<br \/>d) \\(\\overrightarrow {DE} + \\overrightarrow {BF} \\)<\/li>\n<li>Qual \u00e9 a imagem de B por \\({T_{\\overrightarrow {HF} }}\\)?<\/li>\n<li>Qual \u00e9 a imagem do tri\u00e2ngulo [BEF] por \\({T_{ &#8211; \\overrightarrow {AF} }}\\)?<\/li>\n<li>Qual \u00e9 a imagem do tri\u00e2ngulo [DEF] pela transla\u00e7\u00e3o composta das transla\u00e7\u00f5es \\({T_{\\overrightarrow {FH} }}\\) e \\({T_{\\overrightarrow {BG} }}\\)?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_24135' onClick='GTTabs_show(1,24135)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24135'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag108-6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"24136\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=24136\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag108-6.png\" data-orig-size=\"305,276\" 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_Pag108-6\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag108-6.png\" class=\"alignright wp-image-24136\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag108-6-300x271.png\" alt=\"\" width=\"270\" height=\"244\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag108-6-300x271.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag108-6.png 305w\" sizes=\"auto, (max-width: 270px) 100vw, 270px\" \/><\/a>Na figura est\u00e3o representados seis tri\u00e2ngulos equil\u00e1teros geometricamente iguais.<\/p>\n<ol>\n<li>Um vetor igual a \\(\\overrightarrow {GE} \\) \u00e9 \\(\\overrightarrow {BF} \\), por exemplo.<\/li>\n<li>Um vetor sim\u00e9trico de \\(\\overrightarrow {AF} \\) \u00e9 \\(\\overrightarrow {BF} \\), por exemplo.<\/li>\n<li>Determina:<br \/>a) \\(\\overrightarrow {HB} + \\overrightarrow {BF} = \\overrightarrow {HF} \\)<br \/>b) \\(\\overrightarrow {AF} + \\overrightarrow {BE} = \\overrightarrow {AD} \\)<br \/>c) \\(\\overrightarrow {DG} + \\overrightarrow {BC} = \\overrightarrow {AC} \\)<br \/>d) \\(\\overrightarrow {DE} + \\overrightarrow {BF} = \\overrightarrow 0 \\)<\/li>\n<li>A imagem de B por \\({T_{\\overrightarrow {HF} }}\\) \u00e9 o ponto E.<\/li>\n<li>A imagem do tri\u00e2ngulo [BEF] por \\({T_{ &#8211; \\overrightarrow {AF} }}\\) \u00e9 o tri\u00e2ngulo [ADF].<\/li>\n<li>A imagem do tri\u00e2ngulo [DEF] pela transla\u00e7\u00e3o composta das transla\u00e7\u00f5es \\({T_{\\overrightarrow {FH} }}\\) e \\({T_{\\overrightarrow {BG} }}\\) \u00e9 o tri\u00e2ngulo [BEG].<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_24135' onClick='GTTabs_show(0,24135)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera a figura em que est\u00e3o representados tri\u00e2ngulos equil\u00e1teros geometricamente iguais. Indica um vetor igual a \\(\\overrightarrow {GE} \\). Indica um vetor sim\u00e9trico de \\(\\overrightarrow {AF} \\). Determina:a) \\(\\overrightarrow {HB} +&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":24137,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,685],"tags":[424,67,381,688],"series":[],"class_list":["post-24135","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-translacao","tag-vetores"],"views":191,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag108-6_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24135","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=24135"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24135\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/24137"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24135"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24135"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24135"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24135"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}