{"id":15053,"date":"2020-03-05T15:37:08","date_gmt":"2020-03-05T18:37:08","guid":{"rendered":"https:\/\/beduka.com\/blog\/?p=15053"},"modified":"2020-07-02T10:50:17","modified_gmt":"2020-07-02T13:50:17","slug":"exercicios-sobre-o-teorema-de-pitagoras","status":"publish","type":"post","link":"https:\/\/beduka.com\/blog\/exercicios\/matematica-exercicios\/exercicios-sobre-o-teorema-de-pitagoras\/","title":{"rendered":"Exerc\u00edcios sobre Teorema de Pit\u00e1goras com gabarito"},"content":{"rendered":"\n<p><strong><em>O Teorema de Pit\u00e1goras \u00e9 associado com o comprimento dos lados do tri\u00e2ngulo ret\u00e2ngulo, que \u00e9 formado por um \u00e2ngulo interno de 90\u00b0, denominado \u00e2ngulo reto. A f\u00f3rmula desse teorema \u00e9 a\u00b2= b\u00b2 + c\u00b2.&nbsp; Fa\u00e7a os Exerc\u00edcios sobre Teorema de Pit\u00e1goras.<\/em><\/strong><br><\/p>\n\n\n\n<p>Essa mat\u00e9ria \u00e9 cobrada na prova de Matem\u00e1tica e suas Tecnologias no <a href=\"https:\/\/beduka.com\/blog\/guia-completo-do-enem\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">ENEM<\/a>. Por isso, fazer os exerc\u00edcios sobre Teorema de Pit\u00e1goras e revisar o conte\u00fado vai te preparar ainda mais para os principais vestibulares.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">O que \u00e9 Teorema de Pit\u00e1goras?<\/h2>\n\n\n\n<p>Teorema de Pit\u00e1goras \u00e9 um dos teoremas com maior destaque na Matem\u00e1tica. Ele \u00e9 importante e essencial para a resolu\u00e7\u00e3o de quest\u00f5es que envolvem geometria anal\u00edtica, geometria plana, geometria espacial, trigonometria, etc.<br><\/p>\n\n\n\n<ul><li>Aproveite e confira os nossos <a href=\"https:\/\/beduka.com\/blog\/exercicios\/matematica-exercicios\/exercicios-de-trigonometria\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">exerc\u00edcios de TRIGONOMETRIA.<\/a><\/li><\/ul>\n\n\n\n<p>Teorema de Pit\u00e1goras possui rela\u00e7\u00e3o com o comprimento dos lados do tri\u00e2ngulo ret\u00e2ngulo. O tri\u00e2ngulo ret\u00e2ngulo \u00e9 formado por um \u00e2ngulo interno (90\u00ba), denominado \u00e2ngulo reto.<br><\/p>\n\n\n\n<p>Esse teorema \u00e9 definido pelo seguinte enunciado: \u201ca soma dos quadrados de seus catetos corresponde ao quadrado de sua hipotenusa.&#8221;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Qual a f\u00f3rmula do Teorema de Pit\u00e1goras?<\/h2>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/F\u00f3rmula-do-Teorema-de-Pit\u00e1goras.jpg\" alt=\"F\u00f3rmula-do-Teorema-de-Pit\u00e1goras\" class=\"wp-image-15060\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/F\u00f3rmula-do-Teorema-de-Pit\u00e1goras.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/F\u00f3rmula-do-Teorema-de-Pit\u00e1goras-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/F\u00f3rmula-do-Teorema-de-Pit\u00e1goras-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><figcaption>F\u00f3rmula-do-Teorema-de-Pit\u00e1goras<\/figcaption><\/figure><\/div>\n\n\n\n<p>Como o pr\u00f3prio enunciado j\u00e1 diz:<\/p>\n\n\n\n<p><br><strong>a\u00b2= b\u00b2 + c\u00b2<\/strong><br><\/p>\n\n\n\n<p><strong>Sendo:<\/strong><br><\/p>\n\n\n\n<p><strong>a:<\/strong> hipotenusa (maior lado do tri\u00e2ngulo ret\u00e2ngulo e est\u00e1 no lado oposto ao \u00e2ngulo reto);<\/p>\n\n\n\n<p><strong>b: <\/strong>cateto (medida igual a 90\u00ba);<\/p>\n\n\n\n<p><strong>c: <\/strong>cateto (medida igual a 90\u00ba).<br><br><\/p>\n\n\n\n<p>Veja a representa\u00e7\u00e3o abaixo:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/Pit\u00e1goras_catetos_e_hipotenusa.jpg\" alt=\"Pit\u00e1goras_catetos_e_hipotenusa\" class=\"wp-image-15061\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/Pit\u00e1goras_catetos_e_hipotenusa.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/Pit\u00e1goras_catetos_e_hipotenusa-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/Pit\u00e1goras_catetos_e_hipotenusa-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/div>\n\n\n\n<p>Os catetos s\u00e3o separados em oposto e adjacente, sendo isso definido a partir da posi\u00e7\u00e3o de cada um. O cateto que est\u00e1 unido ao \u00e2ngulo de refer\u00eancia, \u00e9 definido de <strong>cateto adjacente, <\/strong>ou seja, se ele est\u00e1 contr\u00e1rio, denominamos de <strong>cateto oposto. Veja:<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/Catetos-adjacente-e-oposto-e-hipotenusa-no-Teorema-de-Pit\u00e1goras.jpg\" alt=\"Catetos-adjacente-e-oposto-e-hipotenusa-no-Teorema-de-Pit\u00e1goras\" class=\"wp-image-15062\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/Catetos-adjacente-e-oposto-e-hipotenusa-no-Teorema-de-Pit\u00e1goras.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/Catetos-adjacente-e-oposto-e-hipotenusa-no-Teorema-de-Pit\u00e1goras-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/Catetos-adjacente-e-oposto-e-hipotenusa-no-Teorema-de-Pit\u00e1goras-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">O que \u00e9 Tri\u00e2ngulo Pitag\u00f3rico?<\/h2>\n\n\n\n<p>Pode ocorrer, que as medidas dos lados de um tri\u00e2ngulo ret\u00e2ngulo sejam caracterizados por n\u00fameros inteiros positivos. Caso isso aconte\u00e7a, o tri\u00e2ngulo passa a ser denominado tri\u00e2ngulo pitag\u00f3rico.<br><\/p>\n\n\n\n<p>Ent\u00e3o, os catetos, juntamente com a hipotenusa s\u00e3o chamados <strong>\u201cterno pitag\u00f3rico\u201d<\/strong> ou <strong>\u201ctrio pitag\u00f3rico\u201d<\/strong>. Para confirmar se os tr\u00eas n\u00fameros formam de fato o trio pitag\u00f3rico, \u00e9 necess\u00e1rio usar a f\u00f3rmula:<\/p>\n\n\n\n<p><br><strong>a\u00b2 = b\u00b2 + c\u00b2<\/strong><br><\/p>\n\n\n\n<p>O trio pitag\u00f3rico que merece mais destaque, \u00e9 composto pelos seguintes numerais: 3 (cateto oposto), 4 (cateto adjacente), 5 (hipotenusa).&nbsp;<br><\/p>\n\n\n\n<p>Perceba que os m\u00faltiplos desses n\u00fameros citados, formam um terno pitag\u00f3rico. Ent\u00e3o se multiplicarmos por 3 o trio 3, 4 e 5, passa a ser 9, 12 e 15. Logo tamb\u00e9m formar\u00e1 terno pitag\u00f3rico.<br><\/p>\n\n\n\n<p>Outros ternos que podemos citar s\u00e3o:<br><\/p>\n\n\n\n<ul><li>5, 12, 13.<\/li><li>7, 24, 25.<\/li><li>20, 21, 29.<\/li><li>12, 35, 37.<\/li><\/ul>\n\n\n\n<p>Agora fa\u00e7a os exerc\u00edcios sobre Teorema de Pit\u00e1goras para fixar ainda mais a mat\u00e9ria!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Exerc\u00edcios sobre Teorema de Pit\u00e1goras<\/h2>\n\n\n\n<p><strong>1 &#8211; (IFSC\/2015) &#8211;<\/strong> Para acessar o topo de uma plataforma de saltos a 400 cm de altura, um atleta deve subir uma escadaria que possui 8 degraus no primeiro lance e 6 degraus no segundo lance de escada, conforme mostra a figura ao lado. Sabendo que cada degrau possui 30 cm de profundidade, \u00e9 CORRETO afirmar que o comprimento, em cm, da haste met\u00e1lica AB utilizada para dar sustenta\u00e7\u00e3o \u00e0 plataforma \u00e9:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"324\" height=\"380\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/exercicio-pitagoras-vestibular-ifsc-2015.jpg\" alt=\"exercicio-pitagoras-vestibular-ifsc-2015\" class=\"wp-image-15054\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/exercicio-pitagoras-vestibular-ifsc-2015.jpg 324w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/exercicio-pitagoras-vestibular-ifsc-2015-256x300.jpg 256w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/exercicio-pitagoras-vestibular-ifsc-2015-320x375.jpg 320w\" sizes=\"(max-width: 324px) 100vw, 324px\" \/><\/figure><\/div>\n\n\n\n<p>a) 300<\/p>\n\n\n\n<p>b) 400<\/p>\n\n\n\n<p>c) 500<\/p>\n\n\n\n<p>d) 200<\/p>\n\n\n\n<p>e) 100<br><\/p>\n\n\n\n<p><strong>2 &#8211; (IFSP\/2015) &#8211;<\/strong> O transporte alternativo \u00e9 uma maneira de se locomover usando um meio diferente dos mais tradicionais. A bicicleta \u00e9 um exemplo disso. Em alguns lugares, ela \u00e9 usada porque \u00e9 mais barata, como no interior do Brasil e em pa\u00edses como a \u00cdndia e China. Outras pessoas escolhem andar de bicicleta por uma quest\u00e3o ideol\u00f3gica, porque elas n\u00e3o agridem o meio ambiente e n\u00e3o causam tantos transtornos quanto os carros. Usando uma bicicleta, uma pessoa sai do ponto A e se dirige ao ponto B. O percurso, dado em km, representado pelos segmentos AC, CD e DB est\u00e1 esbo\u00e7ado no gr\u00e1fico abaixo.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"380\" height=\"325\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/teorema-de-pitagoras-distancia-entre-dois-pontos-ifsp-2015.jpg\" alt=\"teorema-de-pitagoras-distancia-entre-dois-pontos-ifsp-2015\" class=\"wp-image-15055\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/teorema-de-pitagoras-distancia-entre-dois-pontos-ifsp-2015.jpg 380w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/teorema-de-pitagoras-distancia-entre-dois-pontos-ifsp-2015-300x257.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/teorema-de-pitagoras-distancia-entre-dois-pontos-ifsp-2015-320x274.jpg 320w\" sizes=\"(max-width: 380px) 100vw, 380px\" \/><\/figure><\/div>\n\n\n\n<p>Considerando \u221a2 = 1,4, assinale a alternativa que apresenta a dist\u00e2ncia percorrida pela pessoa do ponto A ao ponto B.<br><\/p>\n\n\n\n<p>a) 56 km.<\/p>\n\n\n\n<p>b) 21 km.<\/p>\n\n\n\n<p>c) 20 km.<\/p>\n\n\n\n<p>d) 15 km.<\/p>\n\n\n\n<p>e) 10 km.<br><\/p>\n\n\n\n<p><strong>3 &#8211; (UFRN) &#8211; <\/strong>Um objeto desloca-se 10m no sentido oeste-leste sobre um plano, a partir de uma posi\u00e7\u00e3o inicial. Em seguida, percorre mais 20m no sentido sul-norte, 30m no sentido leste-oeste, 40m no sentido norte-sul, 50m no sentido oeste-leste e 60m no sentido sul-norte. A dist\u00e2ncia entre a posi\u00e7\u00e3o inicial e a posi\u00e7\u00e3o final \u00e9:<br><\/p>\n\n\n\n<p>a)&nbsp; 2\u221a2<\/p>\n\n\n\n<p>b)&nbsp; 2(\u221a2\u22121)<\/p>\n\n\n\n<p>c)&nbsp; 2(\u221a2+1)<\/p>\n\n\n\n<p>d)&nbsp; 2\u221a2\u22121<\/p>\n\n\n\n<p>e)&nbsp; 2\u221a2+1<br><\/p>\n\n\n\n<p><strong>4 &#8211; (FATEC) &#8211; <\/strong>O valor do raio da circunfer\u00eancia da figura \u00e9:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"512\" height=\"380\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/exerc\u00edcio-vestibular-teorema-de-pitagoras-na-circunferencia-ufrn.png\" alt=\"exerc\u00edcio-vestibular-teorema-de-pitagoras-na-circunferencia-fatec\" class=\"wp-image-15056\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/exerc\u00edcio-vestibular-teorema-de-pitagoras-na-circunferencia-ufrn.png 512w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/exerc\u00edcio-vestibular-teorema-de-pitagoras-na-circunferencia-ufrn-300x223.png 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/exerc\u00edcio-vestibular-teorema-de-pitagoras-na-circunferencia-ufrn-320x238.png 320w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/figure><\/div>\n\n\n\n<p>a)&nbsp; 7,5<\/p>\n\n\n\n<p>b)&nbsp; 14,4<\/p>\n\n\n\n<p>c)&nbsp; 12,5<\/p>\n\n\n\n<p>d)&nbsp; 9,5<\/p>\n\n\n\n<p>e)&nbsp; 10,0<br><\/p>\n\n\n\n<p><strong>5 &#8211; (ENEM) &#8211; <\/strong>Na figura abaixo, que representa o projeto de uma escada com 5 degraus de mesma altura, o comprimento total do corrim\u00e3o \u00e9 igual a:<br><br><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"322\" height=\"224\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/exercicios-de-teorema-de-pitagoras-do-enem.png\" alt=\"exercicios-de-teorema-de-pitagoras-do-enem\" class=\"wp-image-15057\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/exercicios-de-teorema-de-pitagoras-do-enem.png 322w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/exercicios-de-teorema-de-pitagoras-do-enem-300x209.png 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/03\/exercicios-de-teorema-de-pitagoras-do-enem-320x223.png 320w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><\/figure><\/div>\n\n\n\n<p>a) 1,8 m<br>b) 1,9 m<br>c) 2,0 m<br>d) 2,1 m<br>e) 2,2 m<br><\/p>\n\n\n\n<p>Baixe o melhor <a href=\"https:\/\/beduka.com\/blog\/enem\/plano-de-estudos-gratuito\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">plano de estudos gratuito<\/a> que voc\u00ea encontrar\u00e1 na internet.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Respostas dos Exerc\u00edcios sobre Teorema de Pit\u00e1goras<\/h2>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 1 &#8211;<\/strong><\/p>\n\n\n\n<p>c) 500<br><\/p>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 2 &#8211;<\/strong><\/p>\n\n\n\n<p>a) 56 km.<br><\/p>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 3 &#8211;<\/strong><\/p>\n\n\n\n<p>b)&nbsp; 2(\u221a2\u22121)<br><\/p>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 4 &#8211;<\/strong><\/p>\n\n\n\n<p>c)&nbsp; 12,5<br><\/p>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 5 &#8211;<\/strong><\/p>\n\n\n\n<p>d) 2,1 m<br><\/p>\n\n\n\n<p>Estude para o Enem com o<a href=\"https:\/\/beduka.com\/simulado\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\"> Simulado Beduka.<\/a> <strong>\u00c9 gratuito!<\/strong><br><\/p>\n\n\n\n<p>Gostou dos nossos Exerc\u00edcios sobre Teorema de Pit\u00e1goras? Compartilhe com os seus amigos e comente abaixo sobre \u00e1reas que voc\u00ea deseja mais explica\u00e7\u00f5es.<br><\/p>\n\n\n\n<p>Queremos te ajudar a encontrar a <strong>FACULDADE IDEAL! <\/strong>Logo abaixo, fa\u00e7a uma pesquisa por curso e cidade que te mostraremos todas as faculdades que podem te atender. <strong>Informamos a nota de corte, valor de mensalidade, nota do MEC, avalia\u00e7\u00e3o dos alunos, modalidades de ensino e muito mais.<\/strong><br><\/p>\n\n\n\n<p>Experimente agora!<br><\/p>\n","protected":false},"excerpt":{"rendered":"<p>O Teorema de Pit\u00e1goras \u00e9 associado com o comprimento dos lados do tri\u00e2ngulo ret\u00e2ngulo, que \u00e9 formado por um \u00e2ngulo interno de 90\u00b0, denominado \u00e2ngulo reto. A f\u00f3rmula desse teorema \u00e9 a\u00b2= b\u00b2 + c\u00b2.&nbsp; Fa\u00e7a os Exerc\u00edcios sobre Teorema de Pit\u00e1goras. Essa mat\u00e9ria \u00e9 cobrada na prova de Matem\u00e1tica e suas Tecnologias no ENEM. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":15059,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0},"categories":[610],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.10 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Exerc\u00edcios de Teorema de Pit\u00e1goras + Gabarito!<\/title>\n<meta name=\"description\" content=\"Fa\u00e7a agora exerc\u00edcios sobre o Teorema de Pit\u00e1goras. 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