{"id":11454,"date":"2022-07-11T16:43:20","date_gmt":"2022-07-11T11:13:20","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11454"},"modified":"2022-07-11T16:44:49","modified_gmt":"2022-07-11T11:14:49","slug":"abc-is-an-isosceles-triangle-right-angled-at-c-prove-that-ab2-2ac2","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/abc-is-an-isosceles-triangle-right-angled-at-c-prove-that-ab2-2ac2\/","title":{"rendered":"ABC is an isosceles triangle right angled at C. Prove that \\({AB}^2\\) = \\(2{AC}^2\\)."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>Since ABC is an isosceles right triangle, right angled at C, therefore<img decoding=\"async\" loading=\"lazy\" class=\" wp-image-11464 alignright\" src=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-5-4.jpeg?resize=156%2C178&#038;ssl=1\" alt=\"triangle\" width=\"156\" height=\"178\" srcset=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-5-4.jpeg?resize=263%2C300&amp;ssl=1 263w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-5-4.jpeg?resize=899%2C1024&amp;ssl=1 899w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-5-4.jpeg?resize=768%2C875&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-5-4.jpeg?resize=1348%2C1536&amp;ssl=1 1348w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-5-4.jpeg?w=1700&amp;ssl=1 1700w\" sizes=\"(max-width: 156px) 100vw, 156px\" data-recalc-dims=\"1\" \/><\/p>\n<p>\\({AB}^2\\) = \\({AC}^2\\) + \\({BC}^2\\)<\/p>\n<p>Since given that the triangle is isosceles,<\/p>\n<p>\\(\\therefore\\)\u00a0 BC = AC<\/p>\n<p>\\(\\implies\\) \\({AB}^2\\) = \\({AC}^2\\) + \\({AC}^2\\)<\/p>\n<p>So,<strong> \\({AB}^2\\) = \\(2{AC}^2\\)<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : Since ABC is an isosceles right triangle, right angled at C, therefore \\({AB}^2\\) = \\({AC}^2\\) + \\({BC}^2\\) Since given that the triangle is isosceles, \\(\\therefore\\)\u00a0 BC = AC \\(\\implies\\) \\({AB}^2\\) = \\({AC}^2\\) + \\({AC}^2\\) So, \\({AB}^2\\) = \\(2{AC}^2\\)<\/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":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>ABC is an isosceles triangle right angled at C. Prove that \\({AB}^2\\) = \\(2{AC}^2\\). - 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\/abc-is-an-isosceles-triangle-right-angled-at-c-prove-that-ab2-2ac2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"ABC is an isosceles triangle right angled at C. 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Prove that \\({AB}^2\\) = \\(2{AC}^2\\). - Mathemerize","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/abc-is-an-isosceles-triangle-right-angled-at-c-prove-that-ab2-2ac2\/","og_locale":"en_US","og_type":"article","og_title":"ABC is an isosceles triangle right angled at C. 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