{"id":155542,"date":"2022-03-26T00:45:41","date_gmt":"2022-03-25T19:15:41","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/isosceles-triangle-and-equilateral-triangle-proof-of-theorem\/"},"modified":"2022-12-31T14:55:11","modified_gmt":"2022-12-31T09:25:11","slug":"isosceles-triangle-and-equilateral-triangle-proof-of-theorem","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/isosceles-triangle-and-equilateral-triangle\/","title":{"rendered":"Isosceles Triangle and Equilateral Triangle \u2013 Proof of Theorem"},"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\/isosceles-triangle-and-equilateral-triangle\/#About_Triangles\" title=\"About Triangles\">About Triangles<\/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\/isosceles-triangle-and-equilateral-triangle\/#Isosceles_Triangles\" title=\"Isosceles Triangles\">Isosceles Triangles<\/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\/isosceles-triangle-and-equilateral-triangle\/#Properties_of_Isosceles_Triangle\" title=\"Properties of Isosceles Triangle:\">Properties of Isosceles Triangle:<\/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\/isosceles-triangle-and-equilateral-triangle\/#Isosceles_Triangle_Theorem\" title=\"Isosceles Triangle Theorem:\">Isosceles Triangle 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\/isosceles-triangle-and-equilateral-triangle\/#Proving_of_Theorem\" title=\"Proving of Theorem\">Proving of Theorem<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/isosceles-triangle-and-equilateral-triangle\/#Facts_About_Isosceles_Triangle\" title=\"Facts About Isosceles Triangle\">Facts About Isosceles Triangle<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/isosceles-triangle-and-equilateral-triangle\/#Uses_of_Triangle\" title=\"Uses of Triangle\">Uses of Triangle<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/isosceles-triangle-and-equilateral-triangle\/#Equilateral_Triangles\" title=\"Equilateral Triangles\">Equilateral Triangles<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/isosceles-triangle-and-equilateral-triangle\/#Properties_of_Equilateral_Triangle\" title=\"Properties of Equilateral Triangle\">Properties of Equilateral Triangle<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/isosceles-triangle-and-equilateral-triangle\/#Isosceles_Triangle_Theorem-2\" title=\"Isosceles Triangle Theorem:\">Isosceles Triangle Theorem:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/isosceles-triangle-and-equilateral-triangle\/#Solved_Example\" title=\"Solved Example-\">Solved Example-<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/isosceles-triangle-and-equilateral-triangle\/#Difference_between_Isosceles_Triangle_Equilateral_Triangle_and_Scalene_Triangle\" title=\"Difference between Isosceles Triangle, Equilateral Triangle, and Scalene Triangle\">Difference between Isosceles Triangle, Equilateral Triangle, and Scalene Triangle<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"About_Triangles\"><\/span>About Triangles<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A triangle is a three-sided polygon. The sum of the angles in a triangle is 180 degrees. The three angles in a triangle can be named using any three of the following letters: A, B, and C. The angle in the corner of a triangle is always A. The angle next to the angle in the corner is always B. The angle opposite the angle in the corner is always C.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-155541 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/isosceles-triangle-and-equilateral-triangle-proof-of-theorem.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/isosceles-triangle-and-equilateral-triangle-proof-of-theorem.jpg?v=1648235738 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/isosceles-triangle-and-equilateral-triangle-proof-of-theorem-300x212.jpg?v=1648235738 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Isosceles_Triangles\"><\/span>Isosceles Triangles<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>An isosceles triangle is a triangle with two sides of equal length. These triangles are named for their isosceles shape, which is created when both of the triangle&#8217;s base angles are equal in size. This shape is also often referred to as an equilateral triangle, although not all isosceles triangles are equilateral.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Properties_of_Isosceles_Triangle\"><\/span>Properties of Isosceles Triangle:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A triangle is said to be isosceles if it has two sides of the same length. These two sides are called the base and the height. The third side is called the vertex.<\/p>\n<p>The base and height of an isosceles triangle are always the same length. The vertex is always the longest side of the triangle.<\/p>\n<p>An isosceles triangle has two angles that are the same size. These angles are called the base angles. The third angle is called the vertex angle.<\/p>\n<p>The base angles of an isosceles triangle always add up to 180 degrees.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Isosceles_Triangle_Theorem\"><\/span>Isosceles Triangle Theorem:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In an isosceles triangle, the two base angles are equal.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Proving_of_Theorem\"><\/span>Proving of Theorem<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Theorem is proved by contradiction. Suppose that there exists a real number $x$ such that $x<\/p>\n<p>eq a$ for all $a$. We will show that this leads to a contradiction.<\/p>\n<p>Since $x<\/p>\n<p>eq a$ for all $a$, there must be a number $y$ such that $x-y=a$. But then $x=y+a$, which is a contradiction. Therefore, there cannot be a real number $x$ such that $x<\/p>\n<p>eq a$ for all $a$.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Facts_About_Isosceles_Triangle\"><\/span>Facts About Isosceles Triangle<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A triangle is isosceles if it has two sides of equal length. These two sides are called the base and the height. The third side is called the vertex.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Uses_of_Triangle\"><\/span>Uses of Triangle<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Triangles are used in a variety of ways. Some common uses of triangles are in roofing, in metalworking, and in construction. Triangles are also used in navigation and in mathematics.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Equilateral_Triangles\"><\/span>Equilateral Triangles<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Each of the three angles of an equilateral triangle are 60\u00b0.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Properties_of_Equilateral_Triangle\"><\/span>Properties of Equilateral Triangle<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>An equilateral triangle is a triangle that has all three sides of the same length. The angles of an equilateral triangle are also all 60 degrees.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Isosceles_Triangle_Theorem-2\"><\/span>Isosceles Triangle Theorem:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In an isosceles triangle, the two sides that are the same length are called the base and the height. The base is the side that is across from the angle that is not the right angle. The height is the length of the line segment from the base to the vertex of the triangle.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Solved_Example\"><\/span>Solved Example-<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>2<\/p>\n<p>A bag contains 5 red balls and 5 green balls. If two balls are drawn at random, what is the probability that they will both be red?<\/p>\n<p>The probability that the two balls drawn at random will both be red is 5\/10.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Difference_between_Isosceles_Triangle_Equilateral_Triangle_and_Scalene_Triangle\"><\/span>Difference between Isosceles Triangle, Equilateral Triangle, and Scalene Triangle<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>An isosceles triangle has two equal sides. An equilateral triangle has three equal sides. A scalene triangle has three unequal sides.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>About Triangles A triangle is a three-sided polygon. The sum of the angles in a triangle is 180 degrees. The [&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":"Isosceles Triangle and Equilateral Triangle \u2013 Proof of Theorem","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Isosceles Triangle and Equilateral Triangle topic of Maths in details explained by subject experts on infinitylearn.com.","custom_permalink":"maths\/isosceles-triangle-and-equilateral-triangle\/"},"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>Isosceles Triangle and Equilateral Triangle \u2013 Proof of Theorem - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Learn about Isosceles Triangle and Equilateral Triangle topic of Maths in details explained by subject experts 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\/isosceles-triangle-and-equilateral-triangle\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Isosceles Triangle and Equilateral Triangle \u2013 Proof of Theorem - 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