{"id":11394,"date":"2022-07-08T01:22:44","date_gmt":"2022-07-07T19:52:44","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11394"},"modified":"2022-07-08T01:22:45","modified_gmt":"2022-07-07T19:52:45","slug":"if-ad-and-pm-are-medians-of-triangles-abc-and-pqr-respectively-where-triangle-abc-triangle-pqr-prove-that-abover-pq-adover-pm","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/if-ad-and-pm-are-medians-of-triangles-abc-and-pqr-respectively-where-triangle-abc-triangle-pqr-prove-that-abover-pq-adover-pm\/","title":{"rendered":"If AD and PM are medians of triangles ABC and PQR respectively, where \\(\\triangle\\) ABC ~ \\(\\triangle\\) PQR, prove that \\(AB\\over PQ\\) = \\(AD\\over PM\\)."},"content":{"rendered":"

Solution :<\/h2>\n

Given<\/strong> : AD and PM are the medians of triangles ABC and PQR respectively, where \"triangles\"\\(\\triangle\\) ABC ~ \\(\\triangle\\) PQR.<\/p>\n

To Prove<\/strong> : \\(AB\\over PQ\\) = \\(AD\\over PM\\)<\/p>\n

Proof<\/strong>\u00a0 : In triangles ABD and PQM, we have<\/p>\n

\\(\\angle\\) B = \\(\\angle\\) D\u00a0 \u00a0 \u00a0 \u00a0 (because \\(\\triangle\\) ABC ~ \\(\\triangle\\) PQR)<\/p>\n

Since AD and PM are the medians to BC and QR respectively and \\(AB\\over PQ\\) = \\(BC\\over QR\\)<\/p>\n

\\(AB\\over PQ\\) = \\({1\\over2}BC\\over {1\\over 2}QR\\)<\/p>\n

So, \\(AB\\over PQ\\) = \\(BD\\over QM\\)<\/p>\n

\\(\\therefore\\)\u00a0 By SAS similarity,<\/p>\n

\\(\\triangle\\) ABD ~ \\(\\triangle\\) PQM<\/p>\n

So, \\(AB\\over PQ\\) = \\(BD\\over QM\\) = \\(AD\\over PM\\)<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Given : AD and PM are the medians of triangles ABC and PQR respectively, where \\(\\triangle\\) ABC ~ \\(\\triangle\\) PQR. To Prove : \\(AB\\over PQ\\) = \\(AD\\over PM\\) Proof\u00a0 : In triangles ABD and PQM, we have \\(\\angle\\) B = \\(\\angle\\) D\u00a0 \u00a0 \u00a0 \u00a0 (because \\(\\triangle\\) ABC ~ \\(\\triangle\\) PQR) Since AD …<\/p>\n

If AD and PM are medians of triangles ABC and PQR respectively, where \\(\\triangle\\) ABC ~ \\(\\triangle\\) PQR, prove that \\(AB\\over PQ\\) = \\(AD\\over PM\\).<\/span> Read More »<\/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":"\nIf AD and PM are medians of triangles ABC and PQR respectively, where \\(\\triangle\\) ABC ~ \\(\\triangle\\) PQR, prove that \\(AB\\over PQ\\) = \\(AD\\over PM\\). - 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\/if-ad-and-pm-are-medians-of-triangles-abc-and-pqr-respectively-where-triangle-abc-triangle-pqr-prove-that-abover-pq-adover-pm\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If AD and PM are medians of triangles ABC and PQR respectively, where \\(\\triangle\\) ABC ~ \\(\\triangle\\) PQR, prove that \\(AB\\over PQ\\) = \\(AD\\over PM\\). - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : Given : AD and PM are the medians of triangles ABC and PQR respectively, where (triangle) ABC ~ (triangle) PQR. 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