{"id":11374,"date":"2022-07-08T01:08:03","date_gmt":"2022-07-07T19:38:03","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11374"},"modified":"2022-07-08T01:08:06","modified_gmt":"2022-07-07T19:38:06","slug":"in-the-figure-e-is-a-point-on-side-cb-produced-of-an-isosceles-triangle-abc-with-ab-perp-ac-prove-that-triangle-abd-triangle-ecf","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/in-the-figure-e-is-a-point-on-side-cb-produced-of-an-isosceles-triangle-abc-with-ab-perp-ac-prove-that-triangle-abd-triangle-ecf\/","title":{"rendered":"In the figure, E is a point on side CB produced of an isosceles triangle ABC with AB \\(\\perp\\) AC, prove that \\(\\triangle\\) ABD ~ \\(\\triangle\\) ECF."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>Here, \\(\\triangle\\) ABC is an isosceles with AB = AC.<img decoding=\"async\" loading=\"lazy\" class=\" wp-image-11375 alignright\" src=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-3-11.jpeg?resize=195%2C186&#038;ssl=1\" alt=\"triangle\" width=\"195\" height=\"186\" srcset=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-3-11.jpeg?resize=300%2C285&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-3-11.jpeg?resize=1024%2C972&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-3-11.jpeg?resize=768%2C729&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-3-11.jpeg?resize=1536%2C1458&amp;ssl=1 1536w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-3-11.jpeg?w=1700&amp;ssl=1 1700w\" sizes=\"(max-width: 195px) 100vw, 195px\" data-recalc-dims=\"1\" \/><\/p>\n<p>\\(\\therefore\\)\u00a0 \\(\\angle\\) B = \\(\\angle\\) C<\/p>\n<p>In \\(\\triangle\\)s ABD and ECF, we have<\/p>\n<p>\\(\\angle\\) ABD = \\(\\angle\\) ECF\u00a0 \u00a0 \u00a0 \u00a0 [\\(\\because\\) \\(\\angle\\) B = \\(\\angle\\) C]<\/p>\n<p>\\(\\angle\\) ADB = \\(\\angle\\) EFC = 90<\/p>\n<p>\\(\\therefore\\)\u00a0 By AA similarity,<\/p>\n<p><strong>\\(\\triangle\\) ABD ~ \\(\\triangle\\) ECF<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : Here, \\(\\triangle\\) ABC is an isosceles with AB = AC. \\(\\therefore\\)\u00a0 \\(\\angle\\) B = \\(\\angle\\) C In \\(\\triangle\\)s ABD and ECF, we have \\(\\angle\\) ABD = \\(\\angle\\) ECF\u00a0 \u00a0 \u00a0 \u00a0 [\\(\\because\\) \\(\\angle\\) B = \\(\\angle\\) C] \\(\\angle\\) ADB = \\(\\angle\\) EFC = 90 \\(\\therefore\\)\u00a0 By AA similarity, \\(\\triangle\\) ABD ~ \\(\\triangle\\) ECF<\/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>In the figure, E is a point on side CB produced of an isosceles triangle ABC with AB \\(\\perp\\) AC, prove that \\(\\triangle\\) ABD ~ \\(\\triangle\\) ECF. - 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\/in-the-figure-e-is-a-point-on-side-cb-produced-of-an-isosceles-triangle-abc-with-ab-perp-ac-prove-that-triangle-abd-triangle-ecf\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"In the figure, E is a point on side CB produced of an isosceles triangle ABC with AB \\(\\perp\\) AC, prove that \\(\\triangle\\) ABD ~ \\(\\triangle\\) ECF. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : Here, (triangle) ABC is an isosceles with AB = AC. (therefore)\u00a0 (angle) B = (angle) C In (triangle)s ABD and ECF, we have (angle) ABD = (angle) ECF\u00a0 \u00a0 \u00a0 \u00a0 [(because) (angle) B = (angle) C] (angle) ADB = (angle) EFC = 90 (therefore)\u00a0 By AA similarity, (triangle) ABD ~ (triangle) ECF\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/in-the-figure-e-is-a-point-on-side-cb-produced-of-an-isosceles-triangle-abc-with-ab-perp-ac-prove-that-triangle-abd-triangle-ecf\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2022-07-07T19:38:03+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-07-07T19:38:06+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-3-11-300x285.jpeg\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/in-the-figure-e-is-a-point-on-side-cb-produced-of-an-isosceles-triangle-abc-with-ab-perp-ac-prove-that-triangle-abd-triangle-ecf\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/in-the-figure-e-is-a-point-on-side-cb-produced-of-an-isosceles-triangle-abc-with-ab-perp-ac-prove-that-triangle-abd-triangle-ecf\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"In the figure, E is a point on side CB produced of an isosceles triangle ABC with AB \\\\(\\\\perp\\\\) AC, prove that \\\\(\\\\triangle\\\\) ABD ~ \\\\(\\\\triangle\\\\) ECF.\",\"datePublished\":\"2022-07-07T19:38:03+00:00\",\"dateModified\":\"2022-07-07T19:38:06+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/in-the-figure-e-is-a-point-on-side-cb-produced-of-an-isosceles-triangle-abc-with-ab-perp-ac-prove-that-triangle-abd-triangle-ecf\/\"},\"wordCount\":70,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Maths Questions\",\"Similar Triangles Questions\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/in-the-figure-e-is-a-point-on-side-cb-produced-of-an-isosceles-triangle-abc-with-ab-perp-ac-prove-that-triangle-abd-triangle-ecf\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/in-the-figure-e-is-a-point-on-side-cb-produced-of-an-isosceles-triangle-abc-with-ab-perp-ac-prove-that-triangle-abd-triangle-ecf\/\",\"url\":\"https:\/\/mathemerize.com\/in-the-figure-e-is-a-point-on-side-cb-produced-of-an-isosceles-triangle-abc-with-ab-perp-ac-prove-that-triangle-abd-triangle-ecf\/\",\"name\":\"In the figure, E is a point on side CB produced of an isosceles triangle ABC with AB \\\\(\\\\perp\\\\) AC, prove that \\\\(\\\\triangle\\\\) ABD ~ \\\\(\\\\triangle\\\\) ECF. - 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