{"id":11294,"date":"2022-07-01T01:27:29","date_gmt":"2022-06-30T19:57:29","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11294"},"modified":"2022-07-01T01:27:32","modified_gmt":"2022-06-30T19:57:32","slug":"prove-that-the-line-drawn-from-the-mid-point-of-one-side-of-triangle-parallel-to-another-side-bisects-the-third-side","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/prove-that-the-line-drawn-from-the-mid-point-of-one-side-of-triangle-parallel-to-another-side-bisects-the-third-side\/","title":{"rendered":"Prove that the line drawn from the mid-point of one side of triangle parallel to another side bisects the third side."},"content":{"rendered":"

Solution :<\/h2>\n

Given<\/strong> : A triangle ABC in which D is the mid point of side AB and the line DE is drawn parallel to BC, meeting AC in E.\"triangle\"<\/p>\n

To Prove<\/strong> :\u00a0 AE = EC<\/p>\n

Proof<\/strong> : In triangle ABC, DE || BC<\/p>\n

By basic proportionality theorem,<\/p>\n

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

But given that D is the mid point of AB,<\/p>\n

AB = DB\u00a0 \u00a0 \u00a0\\(\\implies\\)\u00a0 \u00a0\\(AD\\over DB\\) = 1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0…….(2)<\/p>\n

From (1) and (2), we obtain that<\/p>\n

\\(AE\\over EC\\) = 1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \\(\\implies\\)\u00a0 \u00a0AE = EC.<\/p>\n

Hence, E bisects AC.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Given : A triangle ABC in which D is the mid point of side AB and the line DE is drawn parallel to BC, meeting AC in E. To Prove :\u00a0 AE = EC Proof : In triangle ABC, DE || BC By basic proportionality theorem, \\(AD\\over DB\\) = \\(AE\\over EC\\)\u00a0 \u00a0 \u00a0 …<\/p>\n

Prove that the line drawn from the mid-point of one side of triangle parallel to another side bisects 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 drawn from the mid-point of one side of triangle parallel to another side bisects 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-drawn-from-the-mid-point-of-one-side-of-triangle-parallel-to-another-side-bisects-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 drawn from the mid-point of one side of triangle parallel to another side bisects the third side. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : Given : A triangle ABC in which D is the mid point of side AB and the line DE is drawn parallel to BC, meeting AC in E. 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