{"id":94974,"date":"2017-01-16T09:09:40","date_gmt":"2017-01-16T11:09:40","guid":{"rendered":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/?p=94974"},"modified":"2026-05-28T18:53:46","modified_gmt":"2026-05-28T20:53:46","slug":"semelhanca-de-poligonos","status":"publish","type":"post","link":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/semelhanca-de-poligonos","title":{"rendered":"Semelhan\u00e7a de pol\u00edgonos"},"content":{"rendered":"<p>A\u00a0<b>similaridade poligonal<\/b>\u00a0\u00e9 uma rela\u00e7\u00e3o geom\u00e9trica em que dois pol\u00edgonos t\u00eam exatamente a mesma forma, mas podem ter tamanhos diferentes.<\/p>\n<p>A\u00a0<b>Semelhan\u00e7a de pol\u00edgonos<\/b>\u00a0ocorre quando duas ou mais figuras geom\u00e9tricas possuem o mesmo formato, mas n\u00e3o necessariamente o mesmo tamanho.<\/p>\n<p><b>Para que dois pol\u00edgonos sejam considerados semelhantes, eles devem ter o mesmo n\u00famero de lados e satisfazer duas condi\u00e7\u00f5es simultaneamente:<\/b><\/p>\n<p><b>\u00c2ngulos correspondentes iguais:<\/b>\u00a0Cada \u00e2ngulo do primeiro pol\u00edgono deve ser exatamente igual ao seu \u00e2ngulo correspondente no segundo pol\u00edgono.<br \/>\n<b>Lados correspondentes proporcionais:<\/b>\u00a0A raz\u00e3o entre os comprimentos dos lados correspondentes deve ser id\u00eantica em todos os lados. Essa raz\u00e3o \u00e9 chamada de fator de escala.<\/p>\n<p>Quando dois pol\u00edgonos t\u00eam todos os lados correspondentes proporcionais e todos os \u00e2ngulos correspondentes congruentes, eles s\u00e3o chamados de pol\u00edgonos semelhantes.<\/p>\n<p><b>Semelhan\u00e7a de pol\u00edgonos<\/b><strong>\u00a0&#8211; Exerc\u00edcio<\/strong><\/p>\n<p><b>Observe estes dois hex\u00e1gonos regulares e responda:<\/b><\/p>\n<p><img decoding=\"async\" class=\"alignleft wp-image-94976 size-full\" title=\"Hex\u00e1gono\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/hexagono2.png\" alt=\"Hex\u00e1gono\" width=\"200\" height=\"205\" \/><\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"alignleft wp-image-94975 size-medium\" title=\"Hex\u00e1gono\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/hexagono1-293x300.png\" alt=\"Hex\u00e1gono\" width=\"293\" height=\"300\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/hexagono1-293x300.png 293w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/hexagono1.png 300w\" sizes=\"(max-width: 293px) 100vw, 293px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><b>a)\u00a0<\/b>Os lados correspondentes s\u00e3o proporcionais?<\/p>\n<p><b>Resposta:<\/b>\u00a0Sim<\/p>\n<p><b>b)<\/b>\u00a0Os \u00e2ngulos correspondentes s\u00e3o congruentes?<\/p>\n<p><b>Resposta:\u00a0<\/b>Sim<\/p>\n<p><b>c)<\/b>\u00a0Esses hex\u00e1gonos s\u00e3o semelhantes?<\/p>\n<p><b>Resposta:<\/b>\u00a0Sim<\/p>\n<p><strong>Observe as figuras:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-94986\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_772-Jan.-16-08.59.jpg\" alt=\"Semelhan\u00e7a de pol\u00edgonos\" width=\"554\" height=\"133\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_772-Jan.-16-08.59.jpg 554w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_772-Jan.-16-08.59-300x72.jpg 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Elas representam ret\u00e2ngulos com escalas diferentes. Observe que os tr\u00eas ret\u00e2ngulos t\u00eam a mesma forma, mas de tamanhos diferentes. Dizemos que esses mapas s\u00e3o figuras semelhantes.<\/p>\n<p><b>Nessas figuras podemos identificar:<\/b><\/p>\n<p>AB \u2013 dist\u00e2ncia entre A e B (comprimento do ret\u00e2ngulo)<\/p>\n<p>CD \u2013 dist\u00e2ncia entre C e D (largura do ret\u00e2ngulo)<\/p>\n<p>\u03b1 \u03b2 \u00a0e\u00a0\u03b3- \u00e2ngulos agudos formados pelos segmentos\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-94990 alignnone\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_773-Jan.-16-09.03.jpg\" alt=\"Semelhan\u00e7a de pol\u00edgonos\" width=\"30\" height=\"21\" \/><\/p>\n<p>Medindo os segmentos de reta <img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-94990 alignnone\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_773-Jan.-16-09.03.jpg\" alt=\"Semelhan\u00e7a de pol\u00edgonos\" width=\"30\" height=\"21\" \/>e <img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-94991 alignnone\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_774-Jan.-16-09.03.jpg\" alt=\"Semelhan\u00e7a de pol\u00edgonos\" width=\"31\" height=\"23\" \/>\u00a0e os \u00e2ngulos \u00a0(\u03b1 \u03b2 \u00a0e\u00a0\u03b3 ) das figuras, podemos organizar a seguinte tabela:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-94992\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_775-Jan.-16-09.05.jpg\" alt=\"Semelhan\u00e7a de pol\u00edgonos\" width=\"408\" height=\"126\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_775-Jan.-16-09.05.jpg 408w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_775-Jan.-16-09.05-300x93.jpg 300w\" sizes=\"(max-width: 408px) 100vw, 408px\" \/><\/p>\n<p>Observe que: \u2022 Os \u00e2ngulos correspondente nas tr\u00eas figuras t\u00eam medidas iguais; \u2022 As medidas dos segmentos correspondentes s\u00e3o proporcionais;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-94996\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_776-Jan.-16-09.05.jpg\" alt=\"Semelhan\u00e7a de pol\u00edgonos\" width=\"266\" height=\"76\" \/><\/p>\n<p><b>Desse exemplo, podemos concluir que duas ou mais figuras s\u00e3o semelhantes em geometria quando:<\/b><\/p>\n<p>Os \u00e2ngulos correspondentes t\u00eam medidas iguais ;<\/p>\n<p>As medidas dos segmentos correspondentes s\u00e3o proporcionais;<\/p>\n<p>Os elementos das figuras s\u00e3o comuns.<\/p>\n<p><strong>Semelhan\u00e7a de pol\u00edgonos:\u00a0<\/strong>Dois pol\u00edgonos s\u00e3o semelhantes quando os \u00e2ngulos correspondentes s\u00e3o congruentes e os lados correspondentes s\u00e3o proporcionais.<\/p>\n<p><b>A defini\u00e7\u00e3o de pol\u00edgonos semelhantes s\u00f3 \u00e9 v\u00e1lida quando ambas as condi\u00e7\u00f5es s\u00e3o satisfeitas:<\/b>\u00a0\u00c2ngulos correspondentes congruentes e lados correspondentes proporcionais. Apenas uma das condi\u00e7\u00f5es n\u00e3o \u00e9 suficiente para indicar a semelhan\u00e7a entre pol\u00edgonos.<\/p>\n<p><strong>Fonte:<\/strong>\u00a0Col\u00e9gio S\u00e3o Francisco\/www.feis.unesp.br<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A\u00a0similaridade poligonal\u00a0\u00e9 uma rela\u00e7\u00e3o geom\u00e9trica em que dois pol\u00edgonos t\u00eam exatamente a mesma forma, mas podem ter tamanhos diferentes. A\u00a0Semelhan\u00e7a de pol\u00edgonos\u00a0ocorre quando duas ou mais figuras geom\u00e9tricas possuem o mesmo formato, mas n\u00e3o necessariamente o mesmo tamanho. Para que dois pol\u00edgonos sejam considerados semelhantes, eles devem ter o mesmo n\u00famero de lados e satisfazer [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[414],"tags":[],"class_list":["post-94974","post","type-post","status-publish","format-standard","hentry","category-matematica"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Semelhan\u00e7a de pol\u00edgonos, Figura, Geom\u00e9trica Semelhan\u00e7a de pol\u00edgonos<\/title>\n<meta name=\"description\" content=\"Semelhan\u00e7a de pol\u00edgonos, Figura, Geom\u00e9trica, Geometria, \u00c2ngulos, Lados, Tamanho, Semelhantes, Exemplo, Exerc\u00edcio, Semelhan\u00e7a de pol\u00edgonos\" \/>\n<meta name=\"robots\" content=\"noindex, follow, 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