{"id":11288,"date":"2022-07-01T01:05:10","date_gmt":"2022-06-30T19:35:10","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11288"},"modified":"2022-07-01T01:05:13","modified_gmt":"2022-06-30T19:35:13","slug":"in-the-figure-de-oq-and-df-or-show-that-ef-qr","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/in-the-figure-de-oq-and-df-or-show-that-ef-qr\/","title":{"rendered":"In the figure, DE || OQ and DF || OR. Show that EF || QR."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>In triangle PQO,<img decoding=\"async\" loading=\"lazy\" class=\" wp-image-11289 alignright\" src=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-2-5.jpeg?resize=213%2C136&#038;ssl=1\" alt=\"similar triangles image\" width=\"213\" height=\"136\" srcset=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-2-5.jpeg?resize=300%2C191&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-2-5.jpeg?resize=1024%2C654&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-2-5.jpeg?resize=768%2C490&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-2-5.jpeg?resize=1536%2C980&amp;ssl=1 1536w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-2-5.jpeg?w=1700&amp;ssl=1 1700w\" sizes=\"(max-width: 213px) 100vw, 213px\" data-recalc-dims=\"1\" \/><\/p>\n<p>Given,\u00a0 \u00a0 \u00a0 \u00a0 DE || OQ<\/p>\n<p>By Basic proportionality theorem, we have<\/p>\n<p>\\(PE\\over EQ\\) = \\(PD\\over DO\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;..(1)<\/p>\n<p>In triangle POR,<\/p>\n<p>Given,\u00a0 \u00a0 \u00a0 \u00a0 DF ||\u00a0 OR<\/p>\n<p>By Basic proportionality theorem, we have<\/p>\n<p>\\(PD\\over DO\\) = \\(PF\\over FR\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;..(2)<\/p>\n<p>From (1) and (2), we obtain that<\/p>\n<p>\\(PE\\over EQ\\) = \\(PF\\over FR\\)<\/p>\n<p>Hence, By converse of basic proportionality theorem, we have<\/p>\n<p><strong>EF || QR<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : In triangle PQO, Given,\u00a0 \u00a0 \u00a0 \u00a0 DE || OQ By Basic proportionality theorem, we have \\(PE\\over EQ\\) = \\(PD\\over DO\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;..(1) In triangle POR, Given,\u00a0 \u00a0 \u00a0 \u00a0 DF ||\u00a0 OR By Basic proportionality theorem, we have \\(PD\\over DO\\) = \\(PF\\over FR\\)\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-de-oq-and-df-or-show-that-ef-qr\/\"> <span class=\"screen-reader-text\">In the figure, DE || OQ and DF || OR. Show that EF || QR.<\/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, DE || OQ and DF || OR. Show that EF || QR. - 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-de-oq-and-df-or-show-that-ef-qr\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"In the figure, DE || OQ and DF || OR. Show that EF || QR. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : In triangle PQO, Given,\u00a0 \u00a0 \u00a0 \u00a0 DE || OQ By Basic proportionality theorem, we have (PEover EQ) = (PDover DO)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;..(1) In triangle POR, Given,\u00a0 \u00a0 \u00a0 \u00a0 DF ||\u00a0 OR By Basic proportionality theorem, we have (PDover DO) = (PFover FR)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;..(2) From &hellip; In the figure, DE || OQ and DF || OR. 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Show that EF || QR. - 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-de-oq-and-df-or-show-that-ef-qr\/","og_locale":"en_US","og_type":"article","og_title":"In the figure, DE || OQ and DF || OR. Show that EF || QR. - Mathemerize","og_description":"Solution : In triangle PQO, Given,\u00a0 \u00a0 \u00a0 \u00a0 DE || OQ By Basic proportionality theorem, we have (PEover EQ) = (PDover DO)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;..(1) In triangle POR, Given,\u00a0 \u00a0 \u00a0 \u00a0 DF ||\u00a0 OR By Basic proportionality theorem, we have (PDover DO) = (PFover FR)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;..(2) From &hellip; In the figure, DE || OQ and DF || OR. Show that EF || QR. 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