{"id":32989,"date":"2023-08-12T21:38:00","date_gmt":"2023-08-12T21:38:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=32989"},"modified":"2023-08-14T05:27:28","modified_gmt":"2023-08-14T05:27:28","slug":"congruence-of-triangles","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/congruence-of-triangles","title":{"rendered":"Congruence of Triangles: Definition, Fact, Examples, FAQs"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-7b4ce261-d3e0-4602-81fb-7bcbdd01269e\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/congruence-of-triangles#0-what-is-the-congruence-of-triangles>What Is the Congruence of Triangles?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/congruence-of-triangles#3-how-to-prove-triangles-are-congruent>How to Prove Triangles Are Congruent<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/congruence-of-triangles#5-what-are-the-5-types-of-triangle-congruence>What Are the 5 Types of Triangle Congruence?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/congruence-of-triangles#10-solved-examples-on-congruence-of-triangles>Solved Examples on Congruence of Triangles<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/congruence-of-triangles#11-practice-problems-on-congruence-of-triangles>Practice Problems on Congruence of Triangles<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/congruence-of-triangles#12-frequently-asked-questions-about-congruence-of-triangles>Frequently Asked Questions about Congruence of Triangles<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-congruence-of-triangles\">What Is the Congruence of Triangles?<\/h2>\n\n\n\n<p><strong>Two triangles are said to be <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/congruent#:~:text=Congruent%20Triangles,and%20angles%20should%20be%20congruent.&amp;text=Therefore%2C%20ABC%20%E2%89%85%20EFG.\"><strong>congruent<\/strong><\/a><strong> if their corresponding sides and corresponding angles are also congruent.<\/strong> <strong>Congruent triangles have the same shape and the same size.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"357\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/congruence-of-triangles.png\" alt=\"Congruence of triangles\" class=\"wp-image-33025\" title=\"Congruence of triangles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/congruence-of-triangles.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/congruence-of-triangles-300x173.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Observe the diagram shown below.&nbsp;<\/p>\n\n\n\n<p>Corresponding sides: AB = DE, AC = DF, and BC = EF<\/p>\n\n\n\n<p>Corresponding angles: \u2220A = \u2220D, \u2220B = \u2220E, and \u2220C = \u2220F.<\/p>\n\n\n\n<p>Thus, two triangles are congruent.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"301\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/congruence-of-triangles-1.png\" alt=\"Congruence of triangles\" class=\"wp-image-33027\" title=\"Congruence of triangles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/congruence-of-triangles-1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/congruence-of-triangles-1-300x146.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>If two figures can be placed precisely over each other, they are said to be \u201ccongruent\u201d figures.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"356\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/congruent-figures.png\" alt=\"Congruent figures\" class=\"wp-image-33028\" title=\"Congruent figures\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/congruent-figures.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/congruent-figures-300x172.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/answer-questions-related-to-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_classify_tri_on_side_pt.png\" alt=\"Answer Questions Related to Triangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Answer Questions Related to Triangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/classify-triangles-and-rectangles-as-closed-shape\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_triangle_rectangle_2_pt.png\" alt=\"Classify Triangles and Rectangles as Closed Shape Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Classify Triangles and Rectangles as Closed Shape Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/classify-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_classify_triangles_pt.png\" alt=\"Classify Triangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Classify Triangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-the-type-of-triangles-based-on-angles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_classify_tri_on_angle_pt.png\" alt=\"Identify the Type of Triangles Based on Angles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify the Type of Triangles Based on Angles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-triangles-and-rectangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_amusement_park_18_20_gm.png\" alt=\"Identify Triangles and Rectangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Triangles and Rectangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-triangles-and-squares\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_triangles_squares_pt.png\" alt=\"Identify Triangles and Squares Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Triangles and Squares Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-types-of-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_types_of_triangles_pt.png\" alt=\"Identify Types of Triangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Types of Triangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/match-triangles-and-squares\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_amusement_park_4_5_gm.png\" alt=\"Match Triangles and Squares Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Match Triangles and Squares Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/triangles-and-rectangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_triangle_rectangle_1_pt.png\" alt=\"Triangles and Rectangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Triangles and Rectangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-congruent-triangles-definition\">Congruent Triangles Definition<\/h2>\n\n\n\n<p>Two triangles are said to be congruent if three sides and three angles of one triangle are congruent with the corresponding sides and angles of the other triangle.&nbsp;<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/rectangles-and-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/rectangles-and-triangles.jpeg\" alt=\"Rectangles and Triangles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/separate-out-the-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/separate-out-the-triangles.jpeg\" alt=\"Separate Out the Triangles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-symbol-of-congruence\">Symbol of Congruence<\/h2>\n\n\n\n<p>Congruence is represented by the symbol \u201c\u2245.\u201d<\/p>\n\n\n\n<p>Since congruence in objects implies equal shape and size; the symbol of congruence is made of two symbols, one above the other. There is a symbol of tilde \u201c~,\u201d which represents similarity in shape and \u201c=\u201d represents equality in size.&nbsp;<\/p>\n\n\n\n<p>Hence, congruence is represented by the symbol as \u201c\u2245.\u201d<\/p>\n\n\n\n<p>If two triangles are congruent to each other, we will represent it as \u25b3ABC \u2245 \u25b3PQR.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-how-to-prove-triangles-are-congruent\">How to Prove Triangles Are Congruent<\/h2>\n\n\n\n<p>A triangle has 3 sides and 3 angles. For two triangles to be congruent, all 3 sides and angles should be congruent.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"322\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/congruence-of-triangles-proof.png\" alt=\"Congruence of triangles proof\" class=\"wp-image-33029\" title=\"Congruence of triangles proof\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/congruence-of-triangles-proof.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/congruence-of-triangles-proof-300x156.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Let\u2019s prove \u25b3ABC is congruent to \u25b3EFG.<\/p>\n\n\n\n<p>We observe that:<\/p>\n\n\n\n<p>AC = EG<\/p>\n\n\n\n<p>AB = EF&nbsp;<\/p>\n\n\n\n<p>BC = FG&nbsp;<\/p>\n\n\n\n<p>and<\/p>\n\n\n\n<p>\u2220A = \u2220E,<\/p>\n\n\n\n<p>\u2220B = \u2220F<\/p>\n\n\n\n<p>\u2220C = \u2220G<\/p>\n\n\n\n<p>Therefore, \u25b3ABC&nbsp; \u2245 \u25b3EFG<\/p>\n\n\n\n<p>Whenever two or more triangles are congruent, their corresponding sides and angles are also congruent by the rule of Corresponding Parts of Congruent Triangles (CPCT).<\/p>\n\n\n\n<p>To prove the congruence of two triangles we can apply the condition of congruence, which is discussed in the next section.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-conditions-of-congruence-in-triangles\">Conditions of Congruence in Triangles<\/h2>\n\n\n\n<p>Two <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/triangle\">triangles<\/a> are said to be congruent if their corresponding sides and angles are also congruent. We need not measure all the sides and angles of two triangles to check if they are congruent or not. There are five conditions for two triangles to be congruent, SSS, SAS, ASA, AAS, and RHS. If they follow any one of the given criteria, then they are congruent.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-what-are-the-5-types-of-triangle-congruence\">What Are the 5 Types of Triangle Congruence?<\/h2>\n\n\n\n<p>The five types of triangle congruence criteria are as follows<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>SSS triangle congruence (Side-Side-Side)<\/li>\n\n\n\n<li>SAS triangle congruence (Side-Angle-Side)&nbsp;<\/li>\n\n\n\n<li>ASA triangle congruence (Angle-Side-Angle)&nbsp;<\/li>\n\n\n\n<li>AAS triangle congruence (Angle-Angle-Side)&nbsp;<\/li>\n\n\n\n<li>RHS triangle congruence( Right angle-Hypotenuse-Side)<\/li>\n<\/ul>\n\n\n\n<p><strong>SSS Criterion for Triangle Congruence<\/strong><\/p>\n\n\n\n<p>Two triangles ABC and PQR are said to be congruent by SSS criteria if their corresponding sides are equal.&nbsp;<\/p>\n\n\n\n<p>In the following image, we have<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>AB = PQ<\/li>\n\n\n\n<li>BC = QR<\/li>\n\n\n\n<li>AC = PR<\/li>\n<\/ul>\n\n\n\n<p>Thus, by SSS criterion, \u25b3ABC \u2245 \u25b3PQR.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"475\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/sss-criterion-for-congruence.png\" alt=\"SSS criterion for congruence\" class=\"wp-image-33030\" title=\"SSS criterion for congruence\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/sss-criterion-for-congruence.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/sss-criterion-for-congruence-300x230.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>SAS Criterion for\u00a0 Triangle Congruence<\/strong><\/p>\n\n\n\n<p>Two triangles ABC and PQR are said to be congruent by SAS criteria if two of their corresponding sides and the angle included between them are equal.&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>AB = PQ<\/li>\n\n\n\n<li>\u2220A = \u2220P<\/li>\n\n\n\n<li>AC = PR<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"433\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/sas-criterion-for-congruence.png\" alt=\"SAS criterion for congruence\" class=\"wp-image-33031\" title=\"SAS criterion for congruence\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/sas-criterion-for-congruence.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/sas-criterion-for-congruence-300x210.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>ASA Criterion for Triangle Congruence<\/strong><\/p>\n\n\n\n<p>Two triangles ABC and PQR are said to be congruent by ASA criteria if any two angles and the side included between the angles are equal.&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2220B = \u2220Q<\/li>\n\n\n\n<li>BC = QR<\/li>\n\n\n\n<li>\u2220C = \u2220R<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"342\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/asa-criterion-for-congruence.png\" alt=\"ASA criterion for congruence\" class=\"wp-image-33032\" title=\"ASA criterion for congruence\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/asa-criterion-for-congruence.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/asa-criterion-for-congruence-300x165.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>AAS Criterion for Triangle Congruence<\/strong><\/p>\n\n\n\n<p>Two triangles ABC and PQR are said to be congruent by AAS criteria if any two of their corresponding angles and any non-included side are equal.&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2220B = \u2220E<\/li>\n\n\n\n<li>\u2220C = \u2220F<\/li>\n\n\n\n<li>AC = DF<\/li>\n<\/ul>\n\n\n\n<p>Thus, triangles ABC and DEF are congruent by AAS criterion.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"319\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/aas-criterion-for-congruence.png\" alt=\"AAS criterion for congruence\" class=\"wp-image-33033\" title=\"AAS criterion for congruence\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/aas-criterion-for-congruence.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/aas-criterion-for-congruence-300x154.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>RHS or HL Criterion for Triangle Congruence<\/strong><\/p>\n\n\n\n<p>Two right triangles ABC and XYZ are said to be congruent by RHS or HL criteria if their corresponding hypotenuse and one pair of corresponding sides are equal.&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2220B = \u2220Y (right angle)<\/li>\n\n\n\n<li>AC = XZ (hypotenuse)<\/li>\n\n\n\n<li>AB = XY (side)<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"591\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/rhs-criterion-for-congruence.png\" alt=\"RHS criterion for congruence\" class=\"wp-image-33034\" title=\"RHS criterion for congruence\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/rhs-criterion-for-congruence.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/rhs-criterion-for-congruence-300x286.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-congruent-triangles-examples\">Congruent Triangles Examples<\/h2>\n\n\n\n<p>Here are a few examples of congruent triangles with different criteria.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"502\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/congruent-triangles-criteria-with-examples.png\" alt=\"Congruent triangles criteria with examples\" class=\"wp-image-33035\" title=\"Congruent triangles criteria with examples\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/congruent-triangles-criteria-with-examples.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/congruent-triangles-criteria-with-examples-300x243.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-cpctc-rule\">CPCTC Rule<\/h2>\n\n\n\n<p>The <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/cpctc\">CPCTC<\/a> theorem is one of the important triangle congruence theorems. It states that when two triangles are congruent, then every corresponding part of one triangle is congruent to the other.&nbsp;<\/p>\n\n\n\n<p>(CPCTC: Congruent Parts of Congruent Triangles are Congruent.)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-facts-about-congruence-of-triangles\">Facts about Congruence of Triangles<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>Congruent triangles can be flipped over and joined along one side to form a parallelogram or quadrilateral.<\/li>\n\n\n\n<li>In most bridges, congruent triangles are used to maintain a balanced weight.<\/li>\n\n\n\n<li>Additionally, these triangles are also used in the construction of enormous structures throughout the world.<\/li>\n\n\n\n<li>There is no AAA criterion since two triangles with three congruent triangles may or may not have the same shape.<\/li>\n\n\n\n<li>Area and perimeter of two congruent triangles are the same.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we have learned about congruence of triangles, <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/types-of-triangle\">types of triangles<\/a> congruence, conditions of congruence, important facts about triangles congruence, frequently asked questions and examples.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-solved-examples-on-congruence-of-triangles\">Solved Examples on Congruence of Triangles<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Determine whether the triangles listed below are congruent or not, and identify the criterion test for triangle congruence.<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"143\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/sss-criterion-for-congruence-example.png\" alt=\"SSS criterion for congruence example\" class=\"wp-image-33036\" title=\"SSS criterion for congruence example\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>In the above triangle, we have<\/p>\n\n\n\n<p>AB = DE = 7 in \u2026 side<\/p>\n\n\n\n<p>BC = EF = 4 in \u2026 side<\/p>\n\n\n\n<p>AC = DF = 5 in \u2026 side<\/p>\n\n\n\n<p>Hence, we can say that \u0394 ABC \u2245 \u0394 DEF by the SSS congruence criteria.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li><strong>Determine whether the triangles listed below are congruent or not, and identify the criterion test for triangle congruence.<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"177\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/asa-criterion-for-congruence-example.png\" alt=\"ASA criterion for congruence example\" class=\"wp-image-33037\" title=\"ASA criterion for congruence example\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>In the above triangle, we have<\/p>\n\n\n\n<p>\u2220A = \u2220P \u2026 angle<\/p>\n\n\n\n<p>AB = PQ = 7 units \u2026included side<\/p>\n\n\n\n<p>\u2220B = \u2220Q \u2026 angle<\/p>\n\n\n\n<p>Now, we can say that \u0394ABC \u2245 \u0394PQR by the ASA congruence criteria.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li><strong>Determine whether the triangles listed below are congruent or not, and identify the criterion test for triangle congruence.<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"175\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/aas-criterion-for-congruence-example.png\" alt=\"AAS criterion for congruence example\" class=\"wp-image-33038\" title=\"AAS criterion for congruence example\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>In the above triangle, we have<\/p>\n\n\n\n<p>\u2220A = \u2220P<\/p>\n\n\n\n<p>\u2220B = \u2220Q<\/p>\n\n\n\n<p>BC = QR = 6 units<\/p>\n\n\n\n<p>Now, we can say that \u0394 ABC \u2245 \u0394 PQR by the AAS congruence criteria.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n<li><strong>Two triangles MNO and XYZ are congruent. Mention the corresponding sides and angles that will be equal.<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"113\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/rhs-criterion-for-congruence-example.png\" alt=\"RHS criterion for congruence example\" class=\"wp-image-33039\" title=\"RHS criterion for congruence example\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given, \u2206MNO \u2245 \u2206XYZ&nbsp;&nbsp;<\/p>\n\n\n\n<p>As per CPCTC, all the three corresponding sides and angles of congruent triangles \u2206MNO and \u2206XYZ will be equal to each other.<\/p>\n\n\n\n<p>Therefore,&nbsp;<\/p>\n\n\n\n<p>MN = XY, NO = YZ, and MO = XZ&nbsp;<\/p>\n\n\n\n<p>Also,&nbsp;<\/p>\n\n\n\n<p>\u2220M = \u2220X, \u2220N = \u2220Y, and \u2220O = \u2220Z<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"5\">\n<li><strong>Find the length of QR and measure \u2220B if \u2206ABC \u2245 \u2206PQR and BC = 7 inches, \u2220Q = 60<\/strong><strong><sup>0<\/sup><\/strong><strong>.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>\u2206ABC \u2245 \u2206PQR<\/p>\n\n\n\n<p>BC = 7 inches,&nbsp; \u2220Q = 60<sup>0<\/sup>.<\/p>\n\n\n\n<p>ln \u0394ABC and \u0394PQR,&nbsp;<\/p>\n\n\n\n<p>By applying the CPCT (Corresponding Parts of Congruent Triangles) rule of congruence, we get<\/p>\n\n\n\n<p>&nbsp;QR = BC = 7 inches<\/p>\n\n\n\n<p>\u2220B = \u2220Q = 60<sup>0<\/sup>.<\/p>\n\n\n\n<p>Hence, length of QR is 7 inches and \u2220B is equal to 60<sup>0<\/sup>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"11-practice-problems-on-congruence-of-triangles\">Practice Problems on Congruence of Triangles<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Congruence of Triangles: Definition, Fact, Examples, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">If two figures have the same shape and size, then they are ______.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">similar<\/div><div class=\"spq_answer_block\" data-value=\"1\">non-similar<\/div><div class=\"spq_answer_block\" data-value=\"2\">congruent<\/div><div class=\"spq_answer_block\" data-value=\"3\">non-Congruent<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: congruent<br\/>If two figures have the same shape and size then they are called congruent figures.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Which of the following is the symbol of congruence?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\leftrightarrow$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$=$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\equiv$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\cong$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\cong$<br\/>The symbol of congruence is $\\cong$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Which of the following is not a congruence criterion of triangles?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">SAS<\/div><div class=\"spq_answer_block\" data-value=\"1\">AAS<\/div><div class=\"spq_answer_block\" data-value=\"2\">ASA<\/div><div class=\"spq_answer_block\" data-value=\"3\">AAA<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: AAA<br\/>AAA is not a congruence criterion of triangles.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">The perimeters and areas of two congruent triangles _________ equal.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">are always<\/div><div class=\"spq_answer_block\" data-value=\"1\">are sometimes<\/div><div class=\"spq_answer_block\" data-value=\"2\">are never<\/div><div class=\"spq_answer_block\" data-value=\"3\">may or may not be<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: are always<br\/>Since, two congruent triangles have the same shape and size. Hence, if two triangles are congruent, then their perimeters and areas are also equal.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Two triangles XYZ and STU are said to be congruent by ASA criteria then which of the following is correct?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">\u2220X = \u2220S<\/div><div class=\"spq_answer_block\" data-value=\"1\">\u2220Z = \u2220U<\/div><div class=\"spq_answer_block\" data-value=\"2\">XZ = SU<\/div><div class=\"spq_answer_block\" data-value=\"3\">All of the above<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: All of the above<br\/>Given, two triangles XYZ and STU are said to be congruent by ASA criteria.<br>\r\nHence, according to CPCT \u2220X = \u2220S, \u2220Z = \u2220U, and XZ = SU all are correct.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Congruence of Triangles: Definition, Fact, Examples, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Congruence of Triangles\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If two figures have the same shape and size, then they are ______.\",\n                    \"text\": \"If two figures have the same shape and size, then they are ______.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"If two figures have the same shape and size then they are called congruent figures.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"similar\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If two figures have the same shape and size then they are called congruent figures.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"non-similar\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If two figures have the same shape and size then they are called congruent figures.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"non-Congruent\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If two figures have the same shape and size then they are called congruent figures.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"congruent\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"If two figures have the same shape and size then they are called congruent figures.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"If two figures have the same shape and size then they are called congruent figures.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is the symbol of congruence?\",\n                    \"text\": \"Which of the following is the symbol of congruence?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The symbol of congruence is $$\\\\cong$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\leftrightarrow$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The symbol of congruence is $$\\\\cong$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$=$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The symbol of congruence is $$\\\\cong$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\equiv$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The symbol of congruence is $$\\\\cong$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\cong$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The symbol of congruence is $$\\\\cong$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The symbol of congruence is $$\\\\cong$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is not a congruence criterion of triangles?\",\n                    \"text\": \"Which of the following is not a congruence criterion of triangles?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"AAA is not a congruence criterion of triangles.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"SAS\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"AAA is not a congruence criterion of triangles.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"AAS\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"AAA is not a congruence criterion of triangles.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"ASA\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"AAA is not a congruence criterion of triangles.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"AAA\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"AAA is not a congruence criterion of triangles.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"AAA is not a congruence criterion of triangles.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The perimeters and areas of two congruent triangles _________ equal.\",\n                    \"text\": \"The perimeters and areas of two congruent triangles _________ equal.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Since, two congruent triangles have the same shape and size. Hence, if two triangles are congruent, then their perimeters and areas are also equal.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"are sometimes\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Since, two congruent triangles have the same shape and size. Hence, if two triangles are congruent, then their perimeters and areas are also equal.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"are never\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Since, two congruent triangles have the same shape and size. Hence, if two triangles are congruent, then their perimeters and areas are also equal.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"may or may not be\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Since, two congruent triangles have the same shape and size. Hence, if two triangles are congruent, then their perimeters and areas are also equal.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"are always\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Since, two congruent triangles have the same shape and size. Hence, if two triangles are congruent, then their perimeters and areas are also equal.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Since, two congruent triangles have the same shape and size. Hence, if two triangles are congruent, then their perimeters and areas are also equal.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Two triangles XYZ and STU are said to be congruent by ASA criteria then which of the following is correct?\",\n                    \"text\": \"Two triangles XYZ and STU are said to be congruent by ASA criteria then which of the following is correct?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Given, two triangles XYZ and STU are said to be congruent by ASA criteria.<br>\r\nHence, according to CPCT \u2220X = \u2220S, \u2220Z = \u2220U, and XZ = SU all are correct.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"\u2220X = \u2220S\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Given, two triangles XYZ and STU are said to be congruent by ASA criteria.<br>\r\nHence, according to CPCT \u2220X = \u2220S, \u2220Z = \u2220U, and XZ = SU all are correct.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"\u2220Z = \u2220U\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Given, two triangles XYZ and STU are said to be congruent by ASA criteria.<br>\r\nHence, according to CPCT \u2220X = \u2220S, \u2220Z = \u2220U, and XZ = SU all are correct.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"XZ = SU\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Given, two triangles XYZ and STU are said to be congruent by ASA criteria.<br>\r\nHence, according to CPCT \u2220X = \u2220S, \u2220Z = \u2220U, and XZ = SU all are correct.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"All of the above\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Given, two triangles XYZ and STU are said to be congruent by ASA criteria.<br>\r\nHence, according to CPCT \u2220X = \u2220S, \u2220Z = \u2220U, and XZ = SU all are correct.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Given, two triangles XYZ and STU are said to be congruent by ASA criteria.<br>\r\nHence, according to CPCT \u2220X = \u2220S, \u2220Z = \u2220U, and XZ = SU all are correct.\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"12-frequently-asked-questions-about-congruence-of-triangles\">Frequently Asked Questions about Congruence of Triangles<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-0b5819c6-2903-4acc-8649-e0c701fd63fa\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-0b5819c6-2903-4acc-8649-e0c701fd63fa\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-0b5819c6-2903-4acc-8649-e0c701fd63fa\"><strong>Can two quadrilaterals be congruent ?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-0b5819c6-2903-4acc-8649-e0c701fd63fa\">\n\n<p>Yes, two quadrilaterals are congruent. Two quadrilaterals are said to be congruent if their four corresponding sides and four corresponding interior angles are equal.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-0b5819c6-2903-4acc-8649-e0c701fd63fa\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-0b5819c6-2903-4acc-8649-e0c701fd63fa\"><strong>What is the meaning of CPCT?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-0b5819c6-2903-4acc-8649-e0c701fd63fa\">\n\n<p>CPCT stands for \u201ccorresponding parts of congruent triangles.\u201d<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-0b5819c6-2903-4acc-8649-e0c701fd63fa\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-0b5819c6-2903-4acc-8649-e0c701fd63fa\"><strong>How does RHS\/HL congruence work?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-0b5819c6-2903-4acc-8649-e0c701fd63fa\">\n\n<p>Two right triangles are said to be congruent by RHS criteria if their corresponding hypotenuse and one pair of corresponding sides are equal.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-0b5819c6-2903-4acc-8649-e0c701fd63fa\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-0b5819c6-2903-4acc-8649-e0c701fd63fa\"><strong>Does AAA congruence exist?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-0b5819c6-2903-4acc-8649-e0c701fd63fa\">\n\n<p>The AAA criterion cannot be used to demonstrate congruence in triangles. There is a chance that two triangles are similar if three of their angles are the same as those of the other triangle. For example, all three angles of two equilateral triangles are the same, but their sides could be different, so they won&#8217;t be congruent instead of having three angles that are similar. Thus, AAA congruence criterion does not exist.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-0b5819c6-2903-4acc-8649-e0c701fd63fa\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-0b5819c6-2903-4acc-8649-e0c701fd63fa\"><strong>What are the major differences between the similarity and congruence of the triangle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-0b5819c6-2903-4acc-8649-e0c701fd63fa\">\n\n<p>Similar shapes can be resized versions of similar shapes, whereas congruent figures have identical lengths. This is the difference between congruence and similarity of triangles. As a result, we can say that a congruent triangle is the same as a similar triangle, whereas a similar triangle can be congruent or not.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Congruence of Triangles? Two triangles are said to be congruent if their corresponding sides and corresponding angles are also congruent. Congruent triangles have the same shape and the same size. Observe the diagram shown below.&nbsp; Corresponding sides: AB = DE, AC = DF, and BC = EF Corresponding angles: \u2220A = \u2220D, &#8230; <a title=\"Congruence of Triangles: Definition, Fact, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/congruence-of-triangles\" aria-label=\"More on Congruence of Triangles: Definition, Fact, Examples, FAQs\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-32989","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/32989","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=32989"}],"version-history":[{"count":7,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/32989\/revisions"}],"predecessor-version":[{"id":33045,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/32989\/revisions\/33045"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=32989"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=32989"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=32989"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}