{"id":155506,"date":"2022-03-26T00:43:18","date_gmt":"2022-03-25T19:13:18","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/mid-point-theorem-statement-proof-examples-and-faqs\/"},"modified":"2024-08-03T17:24:39","modified_gmt":"2024-08-03T11:54:39","slug":"mid-point-theorem-statement-proof-examples-and-faqs","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/mid-point-theorem\/","title":{"rendered":"Mid Point Theorem &#8211; Statement, Proof, Examples, and FAQs"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/mid-point-theorem\/#An_Introduction_to_Midpoint_Theorem\" title=\"An Introduction to Midpoint Theorem\">An Introduction to Midpoint Theorem<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/mid-point-theorem\/#Midpoint_Theorem_Proof\" title=\"Midpoint Theorem Proof\">Midpoint Theorem Proof<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/mid-point-theorem\/#What_is_the_Converse_of_the_Midpoint_Theorem\" title=\"What is the Converse of the Midpoint Theorem?\">What is the Converse of the Midpoint Theorem?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/mid-point-theorem\/#Uses_of_Midpoint_Theorem\" title=\"Uses of Midpoint Theorem\">Uses of Midpoint Theorem<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/mid-point-theorem\/#The_Midpoint_Theorem\" title=\"The Midpoint Theorem\">The Midpoint Theorem<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"An_Introduction_to_Midpoint_Theorem\"><\/span>An Introduction to Midpoint Theorem<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Mid Point Theorem:<\/p>\n<p>The <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/mid-point-theorem\/\">midpoint<\/a> theorem states that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and half the length of the third side.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-155505 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/mid-point-theorem-statement-proof-examples-and-faqs.jpg\" alt=\"Mid Point Theorem - Statement, Proof, Examples, and FAQs\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/mid-point-theorem-statement-proof-examples-and-faqs.jpg?v=1648235595 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/mid-point-theorem-statement-proof-examples-and-faqs-300x212.jpg?v=1648235595 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Midpoint_Theorem_Proof\"><\/span>Midpoint Theorem Proof<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The midpoint theorem states that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and half the length of the third side.<\/p>\n<p>Proof:<\/p>\n<p>Given: ABC is a triangle with midpoints M, N, and P.<\/p>\n<p>Prove: MN is parallel to BC and has length equal to 1\/2 BC.<\/p>\n<p>Step 1: Draw an altitude from point M to side BC. This line, MN, is parallel to BC.<\/p>\n<p>Step 2: Since MN is parallel to BC, it is also the same length as BC.<\/p>\n<p>Step 3: Therefore, MN has length 1\/2 BC.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_the_Converse_of_the_Midpoint_Theorem\"><\/span>What is the Converse of the Midpoint Theorem?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The converse of the midpoint theorem states that if two points are on a line and the distance between them is equal to the sum of their distances from the two endpoints of the line, then the points are the midpoint of the line.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Uses_of_Midpoint_Theorem\"><\/span>Uses of Midpoint Theorem<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The midpoint theorem can be used in a variety of ways. Some examples include:<\/p>\n<ul>\n<li>Finding the midpoint of a line segment<\/li>\n<li>Finding the center of a circle<\/li>\n<li>Finding the midpoint of a triangle<\/li>\n<li>Finding the midpoint of a quadrilateral<\/li>\n<li>Finding the midpoint of a polygon<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"The_Midpoint_Theorem\"><\/span>The Midpoint Theorem<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The Midpoint Theorem states that the midpoint of a segment is equidistant from the endpoints of the segment.<\/p>\n<p>The midpoint theorem states that in any triangle, the midpoint of the hypotenuse is equidistant from the vertices. This theorem is easily proven using basic geometry. First, draw the triangle with the given vertices. Next, draw in the midpoint of the hypotenuse. Finally, draw in the perpendicular bisectors of the other two sides. The intersection of the perpendicular bisectors will be the midpoint of those sides.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>An Introduction to Midpoint Theorem Mid Point Theorem: The midpoint theorem states that the line segment joining the midpoints of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Mid Point Theorem","_yoast_wpseo_title":"%%title%% %%page%%","_yoast_wpseo_metadesc":"Midpoint theorem states that line segment joining the midpoints of two sides of a triangle is parallel to the third side on Infinitylearn.com","custom_permalink":"maths\/mid-point-theorem\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Mid Point Theorem - Statement, Proof, Examples, and FAQs<\/title>\n<meta name=\"description\" content=\"Midpoint theorem states that line segment joining the midpoints of two sides of a triangle is parallel to the third side on Infinitylearn.com\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/mid-point-theorem\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Mid Point Theorem - 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