{"id":11410,"date":"2022-07-08T22:34:49","date_gmt":"2022-07-08T17:04:49","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11410"},"modified":"2022-07-08T22:42:52","modified_gmt":"2022-07-08T17:12:52","slug":"if-the-areas-of-two-similar-triangles-are-equal-then-the-triangles-are-congruent-i-e-equal-and-similar-triangles-are-congruent","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/if-the-areas-of-two-similar-triangles-are-equal-then-the-triangles-are-congruent-i-e-equal-and-similar-triangles-are-congruent\/","title":{"rendered":"If the areas of two similar triangles are equal, then the triangles are congruent, i.e. equal and similar triangles are congruent."},"content":{"rendered":"

Solution :<\/h2>\n

Given<\/strong> : \\(\\triangle\\) ABC ~ \\(\\triangle\\) DEF such that \\(area(\\triangle ABC)\\) = \\(area(\\triangle DEF)\\)\"triangles\"<\/p>\n

To Prove<\/strong> : \\(\\triangle\\) ABC \\(\\cong\\) \\(\\triangle\\)\u00a0 DEF<\/p>\n

Proof<\/strong> : Since, the ratio of the area of two similar triangles is equal to the ratio of the square of\u00a0 two corresponding sides.<\/p>\n

\\(area(\\triangle ABC)\\over area(\\triangle DEF)\\) = \\({AB}^2\\over {DE}^2\\) = \\({AC}^2\\over {DF}^2\\) = \\({BC}^2\\over {EF}^2\\)<\/p>\n

Given, \\(area(\\triangle ABC)\\) = \\(area(\\triangle DEF)\\)<\/p>\n

\\({AB}^2\\over {DE}^2\\) = \\({AC}^2\\over {DF}^2\\) = \\({BC}^2\\over {EF}^2\\) = 1<\/p>\n

\\({AB}^2\\) = \\({DE}^2\\), \\({AC}^2\\) = \\({DF}^2\\) and \\({BC}^2\\) = \\({EF}^2\\)<\/p>\n

AB = DE, AC = DF and BC = EF<\/p>\n

By SSS theorem of congruence,<\/p>\n

\\(\\triangle\\) ABC \\(\\cong\\) \\(\\triangle\\)\u00a0 DEF<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Given : \\(\\triangle\\) ABC ~ \\(\\triangle\\) DEF such that \\(area(\\triangle ABC)\\) = \\(area(\\triangle DEF)\\) To Prove : \\(\\triangle\\) ABC \\(\\cong\\) \\(\\triangle\\)\u00a0 DEF Proof : Since, the ratio of the area of two similar triangles is equal to the ratio of the square of\u00a0 two corresponding sides. \\(area(\\triangle ABC)\\over area(\\triangle DEF)\\) = \\({AB}^2\\over {DE}^2\\) …<\/p>\n

If the areas of two similar triangles are equal, then the triangles are congruent, i.e. equal and similar triangles are congruent.<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,912],"tags":[],"yoast_head":"\nIf the areas of two similar triangles are equal, then the triangles are congruent, i.e. equal and similar triangles are congruent. - Mathemerize<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/if-the-areas-of-two-similar-triangles-are-equal-then-the-triangles-are-congruent-i-e-equal-and-similar-triangles-are-congruent\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If the areas of two similar triangles are equal, then the triangles are congruent, i.e. equal and similar triangles are congruent. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : Given : (triangle) ABC ~ (triangle) DEF such that (area(triangle ABC)) = (area(triangle DEF)) To Prove : (triangle) ABC (cong) (triangle)\u00a0 DEF Proof : Since, the ratio of the area of two similar triangles is equal to the ratio of the square of\u00a0 two corresponding sides. 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