{"id":11456,"date":"2022-07-11T16:46:08","date_gmt":"2022-07-11T11:16:08","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11456"},"modified":"2022-07-11T16:46:12","modified_gmt":"2022-07-11T11:16:12","slug":"abc-is-an-isosceles-triangle-with-ac-bc-if-ab2-2ac2-prove-that-abc-is-a-right-triangle","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/abc-is-an-isosceles-triangle-with-ac-bc-if-ab2-2ac2-prove-that-abc-is-a-right-triangle\/","title":{"rendered":"ABC is an isosceles triangle with AC = BC. If \\({AB}^2\\) = \\(2{AC}^2\\), prove that ABC is a right triangle."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>Since ABC is an isosceles triangle with AC = BC and \\({AB}^2\\) = \\(2{AC}^2\\), therefore,<\/p>\n<p>\\({AB}^2\\) = \\({AC}^2\\) + \\({AC}^2\\)<\/p>\n<p>\\(\\implies\\)\u00a0 \\({AB}^2\\) = \\({AC}^2\\) + \\({BC}^2\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (because AC = BC, given)<\/p>\n<p>\\(\\therefore\\)\u00a0 <strong>\\(\\triangle\\) ABC is right angled at C.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : Since ABC is an isosceles triangle with AC = BC and \\({AB}^2\\) = \\(2{AC}^2\\), therefore, \\({AB}^2\\) = \\({AC}^2\\) + \\({AC}^2\\) \\(\\implies\\)\u00a0 \\({AB}^2\\) = \\({AC}^2\\) + \\({BC}^2\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (because AC = BC, given) \\(\\therefore\\)\u00a0 \\(\\triangle\\) ABC is right angled at C.<\/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 with AC = BC. If \\({AB}^2\\) = \\(2{AC}^2\\), prove that ABC is a right triangle. - 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-with-ac-bc-if-ab2-2ac2-prove-that-abc-is-a-right-triangle\/\" \/>\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 with AC = BC. 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