{"id":154288,"date":"2022-03-25T23:22:06","date_gmt":"2022-03-25T17:52:06","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/right-triangle-congruence-theorem-proof-and-properties\/"},"modified":"2022-12-31T16:48:50","modified_gmt":"2022-12-31T11:18:50","slug":"right-triangle-congruence-theorem-proof-and-properties","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/right-triangle-congruence-theorem\/","title":{"rendered":"Right Triangle Congruence Theorem \u2013 Proof and Properties"},"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\/right-triangle-congruence-theorem\/#Introduction_To_Right_Triangle_Congruence_Theorems\" title=\"Introduction To Right Triangle Congruence Theorems\">Introduction To Right Triangle Congruence Theorems<\/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\/right-triangle-congruence-theorem\/#Properties_of_Right_Triangles\" title=\"Properties of Right Triangles\">Properties of Right 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\/right-triangle-congruence-theorem\/#Congruence_Theorems_To_Prove_Two_Right_Triangles_Are_Congruent\" title=\"Congruence Theorems To Prove Two Right Triangles Are Congruent\">Congruence Theorems To Prove Two Right Triangles Are Congruent<\/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\/right-triangle-congruence-theorem\/#The_LA_Theorem\" title=\"The LA Theorem\">The LA 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\/right-triangle-congruence-theorem\/#Proving_the_LA_Theorem\" title=\"Proving the LA Theorem\">Proving the LA 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\/right-triangle-congruence-theorem\/#The_LL_Theorem\" title=\"The LL Theorem\">The LL Theorem<\/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\/right-triangle-congruence-theorem\/#Proving_the_LL_Theorem\" title=\"Proving the LL Theorem\">Proving the LL Theorem<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Introduction_To_Right_Triangle_Congruence_Theorems\"><\/span>Introduction To Right Triangle Congruence Theorems<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There are three right triangle congruence theorems:<\/p>\n<p>SAS<\/p>\n<p>SSS<\/p>\n<p>AAS<\/p>\n<p>Each of these theorems states that if two right triangles have two sides and the angle between those two sides congruent, then the triangles are congruent.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-154287 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/right-triangle-congruence-theorem-proof-and-properties.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/right-triangle-congruence-theorem-proof-and-properties.jpg?v=1648230722 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/right-triangle-congruence-theorem-proof-and-properties-300x212.jpg?v=1648230722 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Properties_of_Right_Triangles\"><\/span>Properties of Right Triangles<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A right triangle has three properties: the length of its longest side, called the hypotenuse; the length of its shortest side, called the opposite side; and the length of its other side, called the adjacent side.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Congruence_Theorems_To_Prove_Two_Right_Triangles_Are_Congruent\"><\/span>Congruence Theorems To Prove Two Right Triangles Are Congruent<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There are three congruence theorems that can be used to prove that two right triangles are congruent:<\/p>\n<p>The SSS Congruence Theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.<\/p>\n<p>The SAS Congruence Theorem states that if two sides and the angle between them of one triangle are congruent to two sides and the angle between them of another triangle, then the two triangles are congruent.<\/p>\n<p>The Angle-Side-Angle Congruence Theorem states that if two angles and the side between them of one triangle are congruent to two angles and the side between them of another triangle, then the two triangles are congruent.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"The_LA_Theorem\"><\/span>The LA Theorem<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The LA theorem states that a line segment joining two points on a circle is perpendicular to the radius drawn to the points.<\/p>\n<p>Proof<\/p>\n<p>Draw a line segment connecting the points and denote it as .<\/p>\n<p>Extend to intersect the circle at .<\/p>\n<p>Since is on the circle, and is a radius, is perpendicular to .<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Proving_the_LA_Theorem\"><\/span>Proving the LA Theorem<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To show that the LA theorem is true, we will use induction.<\/p>\n<p>Basis: We know that the LA theorem is true for n = 1.<\/p>\n<p>Induction Step: Assume that the LA theorem is true for some value of n. This means that<\/p>\n<p>\\begin{align*}<\/p>\n<p>L &amp;= A + B<\/p>\n<p>\\\\<\/p>\n<p>&amp;= (1 + 2) + (3 + 4)<\/p>\n<p>\\\\<\/p>\n<p>&amp;= 6 + 7<\/p>\n<p>\\\\<\/p>\n<p>&amp;= 13<\/p>\n<p>\\end{align*}<\/p>\n<p>We will now show that the LA theorem is also true for n + 1. This means that<\/p>\n<p>\\begin{align*}<\/p>\n<p>L &amp;= A + B<\/p>\n<p>\\\\<\/p>\n<p>&amp;= (1 + 2) + (3 + 4)<\/p>\n<p>\\\\<\/p>\n<p>&amp;= (1 + 2) + (7 + 8)<\/p>\n<p>\\\\<\/p>\n<p>&amp;= 10 + 15<\/p>\n<p>\\\\<\/p>\n<p>&amp;= 25<\/p>\n<p>\\end{align*}<\/p>\n<h2><span class=\"ez-toc-section\" id=\"The_LL_Theorem\"><\/span>The LL Theorem<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The LL theorem states that every continuous function on a compact space is bounded.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Proving_the_LL_Theorem\"><\/span>Proving the LL Theorem<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The LL theorem is a result in graph theory that states that every connected graph has at least one path between any two vertices in the graph. This theorem can be proved using induction.<\/p>\n<p>The base case of the induction proof is when the graph is a single vertex. In this case, there is a path between any two vertices in the graph.<\/p>\n<p>The induction step of the proof is when the graph is a connected graph with more than one vertex. In this case, the theorem is true if there is a path between any two vertices in the graph. To prove the theorem, it is necessary to show that there is a path between any two vertices in the graph. This can be done by constructing a path between the two vertices.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introduction To Right Triangle Congruence Theorems There are three right triangle congruence theorems: SAS SSS AAS Each of these theorems [&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":"Right Triangle Congruence Theorem","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Right Triangle Congruence Theorem topic of maths in details explained by subject experts on infinitylearn.com.","custom_permalink":"maths\/right-triangle-congruence-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>Right Triangle Congruence Theorem \u2013 Proof and Properties - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Learn about Right Triangle Congruence Theorem 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\/right-triangle-congruence-theorem\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Right Triangle Congruence Theorem \u2013 Proof and Properties - 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