{"id":11299,"date":"2022-07-01T01:35:07","date_gmt":"2022-06-30T20:05:07","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11299"},"modified":"2022-07-01T01:35:10","modified_gmt":"2022-06-30T20:05:10","slug":"prove-that-the-line-joining-the-mid-points-of-two-sides-of-a-triangle-is-parallel-to-the-third-side","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/prove-that-the-line-joining-the-mid-points-of-two-sides-of-a-triangle-is-parallel-to-the-third-side\/","title":{"rendered":"Prove that the line joining the mid-points of two sides of a triangle is parallel to the third side."},"content":{"rendered":"

Solution :<\/h2>\n

Given<\/strong> : A triangle ABC in which D and E are mid point of sides AB and AC respectively.\"triangle\"<\/p>\n

To Prove<\/strong> :\u00a0 DE || BC<\/p>\n

Proof<\/strong> : Since sides AB and AC have D and E as mid points,<\/p>\n

\\(\\therefore\\)\u00a0 \u00a0AD = DB\u00a0 and\u00a0 AE = EC<\/p>\n

\\(\\implies\\)\u00a0 \\(AD\\over DB\\) = 1\u00a0 and\u00a0 \\(AE\\over EC\\) = 1<\/p>\n

\\(\\implies\\)\u00a0 \\(AD\\over DB\\) = \\(AE\\over EC\\)<\/p>\n

Hence, By converse of Basic proportionality theorem,<\/p>\n

DE || BC.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Given : A triangle ABC in which D and E are mid point of sides AB and AC respectively. To Prove :\u00a0 DE || BC Proof : Since sides AB and AC have D and E as mid points, \\(\\therefore\\)\u00a0 \u00a0AD = DB\u00a0 and\u00a0 AE = EC \\(\\implies\\)\u00a0 \\(AD\\over DB\\) = 1\u00a0 and\u00a0 …<\/p>\n

Prove that the line joining the mid-points of two sides of a triangle is parallel to the third side.<\/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":"\nProve that the line joining the mid-points of two sides of a triangle is parallel to the third side. - 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\/prove-that-the-line-joining-the-mid-points-of-two-sides-of-a-triangle-is-parallel-to-the-third-side\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Prove that the line joining the mid-points of two sides of a triangle is parallel to the third side. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : Given : A triangle ABC in which D and E are mid point of sides AB and AC respectively. To Prove :\u00a0 DE || BC Proof : Since sides AB and AC have D and E as mid points, (therefore)\u00a0 \u00a0AD = DB\u00a0 and\u00a0 AE = EC (implies)\u00a0 (ADover DB) = 1\u00a0 and\u00a0 … Prove that the line joining the mid-points of two sides of a triangle is parallel to the third side. 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