{"id":11285,"date":"2022-07-01T00:59:31","date_gmt":"2022-06-30T19:29:31","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11285"},"modified":"2022-07-01T00:59:34","modified_gmt":"2022-06-30T19:29:34","slug":"in-the-figure-if-de-ac-and-df-ae-prove-that-bfover-fe-beover-ec","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/in-the-figure-if-de-ac-and-df-ae-prove-that-bfover-fe-beover-ec\/","title":{"rendered":"In the figure, if DE || AC and DF || AE, prove that \\(BF\\over FE\\) = \\(BE\\over EC\\)."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>In triangle BCA,<img decoding=\"async\" loading=\"lazy\" class=\" wp-image-11286 alignright\" src=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-2-4.jpeg?resize=216%2C139&#038;ssl=1\" alt=\"similar triangles image\" width=\"216\" height=\"139\" srcset=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-2-4.jpeg?resize=300%2C193&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-2-4.jpeg?resize=1024%2C660&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-2-4.jpeg?resize=768%2C495&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-2-4.jpeg?resize=1536%2C990&amp;ssl=1 1536w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-2-4.jpeg?w=1700&amp;ssl=1 1700w\" sizes=\"(max-width: 216px) 100vw, 216px\" data-recalc-dims=\"1\" \/><\/p>\n<p>Given,\u00a0 \u00a0 \u00a0 \u00a0 DE || AC<\/p>\n<p>By Basic proportionality theorem, we have<\/p>\n<p>\\(BE\\over EC\\) = \\(BD\\over DA\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;..(1)<\/p>\n<p>In triangle BEA,<\/p>\n<p>Given,\u00a0 \u00a0 \u00a0 \u00a0 DF ||\u00a0 AE<\/p>\n<p>By Basic proportionality theorem, we have<\/p>\n<p>\\(BF\\over FE\\) = \\(BD\\over DA\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;..(2)<\/p>\n<p>From (1) and (2), we obtain that<\/p>\n<p><strong>\\(BF\\over FE\\) = \\(BE\\over EC\\)<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : In triangle BCA, Given,\u00a0 \u00a0 \u00a0 \u00a0 DE || AC By Basic proportionality theorem, we have \\(BE\\over EC\\) = \\(BD\\over DA\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;..(1) In triangle BEA, Given,\u00a0 \u00a0 \u00a0 \u00a0 DF ||\u00a0 AE By Basic proportionality theorem, we have \\(BF\\over FE\\) = \\(BD\\over DA\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;..(2) From &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/in-the-figure-if-de-ac-and-df-ae-prove-that-bfover-fe-beover-ec\/\"> <span class=\"screen-reader-text\">In the figure, if DE || AC and DF || AE, prove that \\(BF\\over FE\\) = \\(BE\\over EC\\).<\/span> Read More &raquo;<\/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":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>In the figure, if DE || AC and DF || AE, prove that \\(BF\\over FE\\) = \\(BE\\over EC\\). - 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-if-de-ac-and-df-ae-prove-that-bfover-fe-beover-ec\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"In the figure, if DE || AC and DF || AE, prove that \\(BF\\over FE\\) = \\(BE\\over EC\\). - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : In triangle BCA, Given,\u00a0 \u00a0 \u00a0 \u00a0 DE || AC By Basic proportionality theorem, we have (BEover EC) = (BDover DA)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;..(1) In triangle BEA, Given,\u00a0 \u00a0 \u00a0 \u00a0 DF ||\u00a0 AE By Basic proportionality theorem, we have (BFover FE) = (BDover DA)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;..(2) From &hellip; In the figure, if DE || AC and DF || AE, prove that (BFover FE) = (BEover EC). 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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\/in-the-figure-if-de-ac-and-df-ae-prove-that-bfover-fe-beover-ec\/","og_locale":"en_US","og_type":"article","og_title":"In the figure, if DE || AC and DF || AE, prove that \\(BF\\over FE\\) = \\(BE\\over EC\\). - Mathemerize","og_description":"Solution : In triangle BCA, Given,\u00a0 \u00a0 \u00a0 \u00a0 DE || AC By Basic proportionality theorem, we have (BEover EC) = (BDover DA)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;..(1) In triangle BEA, Given,\u00a0 \u00a0 \u00a0 \u00a0 DF ||\u00a0 AE By Basic proportionality theorem, we have (BFover FE) = (BDover DA)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;..(2) From &hellip; In the figure, if DE || AC and DF || AE, prove that (BFover FE) = (BEover EC). 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