{"id":153934,"date":"2022-03-25T22:58:29","date_gmt":"2022-03-25T17:28:29","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/congruence-of-triangles-different-rules\/"},"modified":"2024-09-18T16:01:51","modified_gmt":"2024-09-18T10:31:51","slug":"congruence-of-triangles-different-rules","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/congruence-of-triangles\/","title":{"rendered":"Congruence of Triangles \u2013 Different Rules"},"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\/congruence-of-triangles\/#What_are_Congruent_Triangles\" title=\"What are Congruent Triangles?\">What are Congruent 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\/congruence-of-triangles\/#Conditions_of_Congruent_Triangles\" title=\"Conditions of Congruent Triangles\">Conditions of Congruent Triangles<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/congruence-of-triangles\/#SSS_Criterion_for_Congruent_triangles\" title=\"SSS Criterion for Congruent triangles\">SSS Criterion for Congruent triangles<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/congruence-of-triangles\/#SAS_Criterion_for_Congruent_triangles\" title=\"SAS Criterion for Congruent triangles\">SAS Criterion for Congruent triangles<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/congruence-of-triangles\/#ASA_Criterion_for_Congruent_triangles\" title=\"ASA Criterion for Congruent triangles\">ASA Criterion for Congruent triangles<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/congruence-of-triangles\/#AAS_Criterion_for_Congruent_triangles\" title=\"AAS Criterion for Congruent triangles\">AAS Criterion for Congruent triangles<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/congruence-of-triangles\/#The_RHS_Criterion_for_Congruent_triangles\" title=\"The RHS Criterion for Congruent triangles\">The RHS Criterion for Congruent triangles<\/a><\/li><\/ul><\/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\/congruence-of-triangles\/#Important_Notes_on_Congruent_Triangles\" title=\"Important Notes on Congruent Triangles\">Important Notes on Congruent 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\/congruence-of-triangles\/#Important_Notes_on_Congruent_Triangles-2\" title=\"Important Notes on Congruent Triangles\">Important Notes on Congruent Triangles<\/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\/congruence-of-triangles\/#Overview_of_Congruence_of_Triangles\" title=\"Overview of Congruence of Triangles\">Overview of Congruence of Triangles<\/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\/congruence-of-triangles\/#Congruent_Triangles_FAQs\" title=\"Congruent Triangles FAQs\">Congruent Triangles FAQs<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/congruence-of-triangles\/#What_does_it_mean_for_two_triangles_to_be_congruent\" title=\"What does it mean for two triangles to be congruent?\">What does it mean for two triangles to be congruent?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/congruence-of-triangles\/#What_are_the_criteria_for_proving_triangle_congruence\" title=\"What are the criteria for proving triangle congruence?\">What are the criteria for proving triangle congruence?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/congruence-of-triangles\/#Why_is_AAA_not_a_criterion_for_triangle_congruence\" title=\"Why is AAA not a criterion for triangle congruence?\">Why is AAA not a criterion for triangle congruence?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>Congruent figures are two figures that are identical in shape and size. A common example is two bangles of the same size and shape, which would be congruent. In geometry, two objects are considered congruent if they are exactly the same in every measurement. In the case of congruent triangles, we can say that one triangle is an exact copy of the other.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_are_Congruent_Triangles\"><\/span>What are Congruent Triangles?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Triangles are three-sided polygons, defined by their three angles, three sides, and three vertices. Based on the lengths of their sides, triangles can be classified as equilateral, isosceles, or scalene. When comparing two different triangles, a different set of rules is applied. Congruent triangles are those that are identical in both side lengths and angle measurements.<\/p>\n<p><img loading=\"lazy\" class=\"size-full wp-image-734143 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Congruent-Triangles.jpg\" alt=\"Congruent Triangles\" width=\"390\" height=\"139\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Congruent-Triangles.jpg 390w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Congruent-Triangles-300x107.jpg 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Congruent-Triangles-150x53.jpg 150w\" sizes=\"(max-width: 390px) 100vw, 390px\" \/><\/p>\n<p>For example in \u0394 PQR and \u0394ABC shown below, it is clear that PQ = AB, PR = AC, QR = BC and \u2220P = \u2220A, \u2220Q = \u2220B and \u2220R = \u2220C. Thus we write \u0394 PQR \u2245 \u0394ABC, i.e. the given triangles are Congruent triangles.<\/p>\n<p><img loading=\"lazy\" class=\"size-full wp-image-734143 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Congruent-Triangles.jpg\" alt=\"Congruent Triangles\" width=\"390\" height=\"139\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Congruent-Triangles.jpg 390w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Congruent-Triangles-300x107.jpg 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Congruent-Triangles-150x53.jpg 150w\" sizes=\"(max-width: 390px) 100vw, 390px\" \/><\/p>\n<p>The two triangles need to be of the same size and shape to be Congruent triangles. When we rotate, reflect, and\/ or translate a triangle, its position or appearance seems to be different. In that case, we need to identify the six parts of a triangle and their corresponding parts in the other triangle. Consider \u0394 ABC and \u0394PQR as shown below.<\/p>\n<p><strong>Example of Congruent Triangles<\/strong><\/p>\n<ul>\n<li>The corresponding vertices are A and P, B and Q, C and R.<\/li>\n<li>The corresponding sides are AB = PQ, BC = QR, CA = RP.<\/li>\n<li>The corresponding angles are \u2220A = \u2220P, \u2220B = \u2220Q and \u2220C = \u2220R.<\/li>\n<\/ul>\n<p>By recognizing the corresponding parts of the triangles in question, one can thus verify that \u0394 ABC is congruent to \u0394PQR.<\/p>\n<div class=\"card\" style=\"text-align: center;\"><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/one-stop-solutions-for-school-prep?utm_source=surge&amp;utm_medium=interlinking\"><br \/>\n<img loading=\"lazy\" class=\" lazyloaded\" style=\"width: 100%; border-radius: 10px;\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/one-stop-solution-for-school-exam.jpg\" alt=\"one-stop-solutions school exam\" width=\"1201\" height=\"636\" data-src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/one-stop-solution-for-school-exam.jpg\" \/><\/a><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/one-stop-solutions-for-school-prep?utm_source=surge&amp;utm_medium=interlinking\"><button><strong>One Stop Solutions for School Exam Preparation<\/strong><\/button><\/a><\/p>\n<div style=\"text-align: center;\">Boost your school preparation with our comprehensive guide for CBSE, ICSE, and State Board exams. Get all the resources you need in one place and excel in your academic journey. Discover the ultimate one-stop solution at Infinity Learn today!<\/div>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"Conditions_of_Congruent_Triangles\"><\/span>Conditions of Congruent Triangles<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Two triangles are congruent if they have the same size and shape. However, it is not always necessary for both triangles to have all six corresponding elements match exactly. Based on research, there are five conditions that can prove two triangles are congruent:<\/p>\n<ul>\n<li>SSS (Side-Side-Side)<\/li>\n<li>SAS (Side-Angle-Side)<\/li>\n<li>ASA (Angle-Side-Angle)<\/li>\n<li>AAS (Angle-Angle-Side)<\/li>\n<li>RHS (Right Angle-Hypotenuse-Side)<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"SSS_Criterion_for_Congruent_triangles\"><\/span>SSS Criterion for Congruent triangles<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The SSS criterion stands for the Side-Side-Side criterion of triangle congruence. According to this rule, two triangles are congruent if all three sides of one triangle correspond exactly to the three sides of another triangle. This means that if the lengths of the sides of one triangle are equal to the lengths of the sides of another triangle, then the two triangles are congruent.<\/p>\n<p>For example, if \u0394ABC and \u0394DEF have:<\/p>\n<ol>\n<li>AB = DE<\/li>\n<li>BC = EF<\/li>\n<li>CA = FD<\/li>\n<\/ol>\n<p>Then, by the SSS criterion, \u0394ABC \u2245 \u0394DEF. It means that the two triangles are congruent.<\/p>\n<p style=\"text-align: center;\"><em><strong>Also Check &#8211; <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/equivalent-fractions\/\"><span class=\"post post-post current-item\">Equivalent Fractions<\/span><\/a><\/strong><\/em><\/p>\n<h3><span class=\"ez-toc-section\" id=\"SAS_Criterion_for_Congruent_triangles\"><\/span>SAS Criterion for Congruent triangles<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The SAS criterion, or Side-Angle-Side rule, states that two triangles are congruent if two sides and the angle between them in one triangle are equal to the corresponding two sides and the included angle in another triangle. This means that if two triangles share two pairs of equal sides with an equal angle between them, then the triangles are congruent.<\/p>\n<p>For example, if \u0394ABC and \u0394DEF have:<\/p>\n<ol>\n<li>AB = DE<\/li>\n<li>BC = EF<\/li>\n<li>\u2220B = \u2220E<\/li>\n<\/ol>\n<p>Then, by the SAS criterion, \u0394ABC \u2245 \u0394DEF. This means that the two triangles are congruent.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"ASA_Criterion_for_Congruent_triangles\"><\/span>ASA Criterion for Congruent triangles<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The ASA criterion stands for the Angle-Side-Angle criterion. According to this rule, two triangles are said to be congruent if two angles and the side included between them in one triangle are equal to the corresponding angles and included side in another triangle. This ensures that the triangles are congruent in all aspects.<\/p>\n<p>For example, if \u0394ABC and \u0394DEF have:<\/p>\n<ol>\n<li>\u2220C = \u2220F<\/li>\n<li>BC = EF<\/li>\n<li>\u2220B = \u2220E<\/li>\n<\/ol>\n<p>Then, by the ASA criterion, \u0394ABC \u2245 \u0394DEF. This means that the two triangles are congruent.<\/p>\n<p style=\"text-align: center;\"><em><strong>Must Read &#8211; <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/an-introduction-to-exponents\/\"><span class=\"post post-post current-item\">Exponents<\/span><\/a><\/strong><\/em><\/p>\n<h3><span class=\"ez-toc-section\" id=\"AAS_Criterion_for_Congruent_triangles\"><\/span>AAS Criterion for Congruent triangles<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The Angle-Angle-Side (AAS) criterion is used to determine if two triangles are congruent. According to this criterion, if two triangles have two angles and one side (which is not between the two angles) equal to the corresponding angles and side of another triangle respectively, then the two triangles are congruent.<\/p>\n<p>For example, if \u0394ABC and \u0394DEF have:<\/p>\n<ol>\n<li>\u2220C = \u2220F<\/li>\n<li>\u2220B = \u2220E<\/li>\n<li>AB = DE<\/li>\n<\/ol>\n<p>Then, by the ASA criterion, \u0394ABC \u2245 \u0394DEF. This means that the two triangles are congruent.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"The_RHS_Criterion_for_Congruent_triangles\"><\/span>The RHS Criterion for Congruent triangles<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The Right Angle-Hypotenuse-Side (RHS) criterion is a specific rule for determining the congruence of two right-angled triangles. It is also known as the Hypotenuse-Leg criterion According to this criterion, two right-angled triangles are congruent if:<\/p>\n<ol>\n<li>The hypotenuse of one triangle is equal to the hypotenuse of the other.<\/li>\n<li>One other side of each triangle is also equal.<\/li>\n<\/ol>\n<h2><span class=\"ez-toc-section\" id=\"Important_Notes_on_Congruent_Triangles\"><\/span>Important Notes on Congruent Triangles<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Below are a few important points about the congruent triangles.<\/p>\n<ul>\n<li>Two triangles will be congruent if all three sides and three angles match each other. There are five conditions to determine if two triangles are congruent. These are the criteria of SSS, SAS, ASA, AAS, and RHS.<\/li>\n<li>A triangle can be a larger replica of another one with same angles hence they may not be congruent in reality. Therefore AAA is not a criterion for determining congruence.<\/li>\n<li>Congruence is described by the symbol of \u2245.<\/li>\n<li>Two identical triangles have identical perimeters and areas.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Important_Notes_on_Congruent_Triangles-2\"><\/span>Important Notes on Congruent Triangles<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Below are a few important points about the congruent triangles.<\/p>\n<ul>\n<li>Two triangles will be congruent if all three sides and three angles match each other. There are five conditions to determine if two triangles are congruent. These are the criteria of SSS, SAS, ASA, AAS, and RHS.<\/li>\n<li>A triangle can be a larger replica of another one with same angles hence they may not be congruent in reality. Therefore AAA is not a criterion for determining congruence.<\/li>\n<li>Congruence is described by the symbol of \u2245.<\/li>\n<li>Two identical triangles have identical perimeters and areas.<\/li>\n<\/ul>\n<div class=\"card\" style=\"text-align: center;\"><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/online-mock-tests?utm_source=surge&amp;utm_medium=interlinking\"><br \/>\n<img loading=\"lazy\" class=\" lazyloaded\" style=\"width: 100%; border-radius: 10px;\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/cvc.png\" alt=\"online mock test\" width=\"1201\" height=\"636\" data-src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/cvc.png\" \/><\/a><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/online-mock-tests?utm_source=surge&amp;utm_medium=interlinking\"><button><strong>Online Mock Test<\/strong><\/button><\/a><\/p>\n<div style=\"text-align: center;\">Boost Your Preparation With Our Free Online Mock Tests For IIT-JEE, NEET And CBSE Exams<\/div>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"Overview_of_Congruence_of_Triangles\"><\/span>Overview of Congruence of Triangles<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>The triangle is said to be congruent when its three sides as well as two angles have the same orientation.<\/li>\n<li>CPCT stands for Corresponding Parts of Congruent Triangles.<\/li>\n<li>There is a theorem called <em>CPCT theorem<\/em> which states that two triangles are congruent if they have similar angles and sides, thus their angles are equal and so are their sides.<\/li>\n<li>When all three sides of the first triangle match with those of the second triangle, then such triangles are said to be congruent as per SSS Rule.<\/li>\n<li>ASA rule stipulates that if any two angles along with the included side between them is equivalent respectively to corresponding angles and included side between them; then these triangles are said to be congruent.<\/li>\n<li>In AAS rule, both the angles and the un-included side are equal to the triangle accordingly.<\/li>\n<li>In RHS rule, hypotenuse and one side of a right-angled triangle are measured equal to one side and hypotenuse of another triangle.<\/li>\n<li>The perimeters and areas of comparable triangles are similar.<\/li>\n<li>There is no AAA criteria rule for the congruent rule because one triangle might be an enlarged copy of another triangle even though they might have equal angles.<\/li>\n<li>Two equilateral triangles might have equal angles but the sides of those triangles might be different hence, there is no congruent triangle in the case of triangles with equilateral triangles.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Congruent_Triangles_FAQs\"><\/span>Congruent Triangles FAQs<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_does_it_mean_for_two_triangles_to_be_congruent\"><\/span>What does it mean for two triangles to be congruent?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tTwo triangles are congruent when all their corresponding sides and angles are exactly the same. This means the triangles have the same shape and size, even if they are rotated or flipped. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_are_the_criteria_for_proving_triangle_congruence\"><\/span>What are the criteria for proving triangle congruence?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe five main criteria for triangle congruence are SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and RHS (Right Angle-Hypotenuse-Side).\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Why_is_AAA_not_a_criterion_for_triangle_congruence\"><\/span>Why is AAA not a criterion for triangle congruence?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\t AAA (Angle-Angle-Angle) only shows that two triangles are similar, meaning they have the same shape but can be different in size. For triangles to be congruent, their sides must also be equal. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What does it mean for two triangles to be congruent?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Two triangles are congruent when all their corresponding sides and angles are exactly the same. This means the triangles have the same shape and size, even if they are rotated or flipped.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What are the criteria for proving triangle congruence?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The five main criteria for triangle congruence are SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and RHS (Right Angle-Hypotenuse-Side).\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Why is AAA not a criterion for triangle congruence?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"AAA (Angle-Angle-Angle) only shows that two triangles are similar, meaning they have the same shape but can be different in size. For triangles to be congruent, their sides must also be equal.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>Congruent figures are two figures that are identical in shape and size. A common example is two bangles of 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":"Congruence of Triangles","_yoast_wpseo_title":"Congruence of Triangles \u2013 Different Rules and Types","_yoast_wpseo_metadesc":"Learn about Congruence of Triangles topic of Maths in details explained by subject experts on infinitylearn.com","custom_permalink":"maths\/congruence-of-triangles\/"},"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>Congruence of Triangles \u2013 Different Rules and Types<\/title>\n<meta name=\"description\" content=\"Learn about Congruence of Triangles topic of Maths in details explained by subject experts on infinitylearn.com\" \/>\n<meta name=\"robots\" content=\"index, follow, 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