{"id":1506,"date":"2022-04-19T13:18:25","date_gmt":"2022-04-19T13:18:25","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=1506"},"modified":"2024-04-02T08:37:53","modified_gmt":"2024-04-02T08:37:53","slug":"congruent-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/congruent","title":{"rendered":"Congruent &#8211; Definition with Examples"},"content":{"rendered":"\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\"><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-59596693-ead4-47d9-8503-d2d7ea06967c\" 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\/geometry\/congruent#0-meaning-of-congruent>Meaning of Congruent<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/congruent#8-solved-examples>Solved Examples<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/congruent#9-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/congruent#10-frequently-asked-questions>Frequently Asked Questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-meaning-of-congruent\">Meaning of Congruent<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">If two figures can be placed precisely over each other, they are said to be \u2018congruent\u2019 figures.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"680\" height=\"211\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/congruent-figures.png\" alt=\"congruent figures\" class=\"wp-image-41557\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/congruent-figures.png 680w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/congruent-figures-300x93.png 300w\" sizes=\"auto, (max-width: 680px) 100vw, 680px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">If you place one slice of bread over the other, you will find that both the slices are of equal shape and size.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"680\" height=\"251\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/bread-as-congruent.png\" alt=\"Bread as congruent\" class=\"wp-image-41558\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/bread-as-congruent.png 680w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/bread-as-congruent-300x111.png 300w\" sizes=\"auto, (max-width: 680px) 100vw, 680px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">The term \u201ccongruent\u201d means exactly equal shape and size. This shape and size should remain equal, even when we flip, turn, or rotate the shapes.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-examples-of-congruent-figures\">Examples of Congruent Figures<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"680\" height=\"251\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/two-butterflies-as-congruent-figures.png\" alt=\"two butterflies as congruent figures\" class=\"wp-image-41559\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/two-butterflies-as-congruent-figures.png 680w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/two-butterflies-as-congruent-figures-300x111.png 300w\" sizes=\"auto, (max-width: 680px) 100vw, 680px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>&nbsp;Two butterflies which have equal shape and size&nbsp;<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"680\" height=\"251\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/two-candy-Ice-cream-congruent-figures.png\" alt=\"two Candy Ice Cream congruent figures\" class=\"wp-image-41560\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/two-candy-Ice-cream-congruent-figures.png 680w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/two-candy-Ice-cream-congruent-figures-300x111.png 300w\" sizes=\"auto, (max-width: 680px) 100vw, 680px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Two candy ice creams which represent equal shape and size&nbsp;<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"680\" height=\"251\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/two-lego-bricks-as-congruent-figures.png\" alt=\"two Lego Bricks as congruent figures\" class=\"wp-image-41561\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/two-lego-bricks-as-congruent-figures.png 680w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/two-lego-bricks-as-congruent-figures-300x111.png 300w\" sizes=\"auto, (max-width: 680px) 100vw, 680px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Two lego bricks which represent equal shape and size<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-symbol-of-congruence\">Symbol of Congruence<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Congruence is represented by the symbol- \u2018<\/strong><strong>\u2245<\/strong><strong>\u2019<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">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<strong> \u201c<\/strong><strong>\u201d <\/strong>which represents similarity in shape and <strong>\u201c=\u201d <\/strong>represents equality in size.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Hence, congruence is represented by the symbol as \u2018<\/strong><strong>\u2245<\/strong><strong>\u2019<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">If two objects A and B are congruent to each other, we will write it as: A \u2245 B<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-congruent-line-segments-\">Congruent Line Segments&nbsp;<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Since congruence implies equal shape and size, the line segments will be congruent if their shape and size is the same.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Observe the above image carefully.<strong>&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since both AB and PQ are line segments they are of the same shape. The length of line segment AB is equal to 5 cm and PQ is also equal to 5 cm. Hence, the length of both line segments are equal to each other.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, if two or more lines are equal in length, they are said to be congruent to each other.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the line segments AB and PQ are congruent with each other.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, it will be represented as line segment AB <strong>\u2245<\/strong> line segment PQ.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-congruent-angles-\">Congruent Angles&nbsp;<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"680\" height=\"263\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/congruent-angles.png\" alt=\"congruent angles\" class=\"wp-image-41562\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/congruent-angles.png 680w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/congruent-angles-300x116.png 300w\" sizes=\"auto, (max-width: 680px) 100vw, 680px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">In the above diagram, <strong>\u2220<\/strong><strong> <\/strong>ABC = 40<strong>\u00b0, <\/strong>whereas <strong>\u2220<\/strong><strong> <\/strong>PQR = 40<strong>\u00b0.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">If we superimpose or overlap <strong>\u2220<\/strong><strong> <\/strong>ABC on <strong>\u2220<\/strong><strong> <\/strong>PQR, we will find that both the angles are congruent to each other.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">As per the rule, two angles are congruent if the measures of both the angles are equal to each other.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, <strong>\u2220 <\/strong>ABC <strong>\u2245<\/strong> <strong>\u2220 <\/strong>PQR&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-congruent-circles\">Congruent Circles<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"680\" height=\"263\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/congruent-circles.png\" alt=\"congruent circles\" class=\"wp-image-41563\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/congruent-circles.png 680w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/congruent-circles-300x116.png 300w\" sizes=\"auto, (max-width: 680px) 100vw, 680px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">In the above diagram, the radius of Circle A is represented by radius OR, whereas the radius of Circle B is represented by OP.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The shape of both the circles is the same and the size is also the same as the length of radii OR and OP is equal to 2 cm each.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">As per the condition of congruency, if the radius of two circles are equal in length, then both the circles are congruent to each other. It also means that both the circles can be easily placed over each other.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">To conclude, Circle A is congruent to Circle B, and it can be written as Circle A &nbsp;<strong>\u2245<\/strong> Circle B.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-congruent-triangles\">Congruent Triangles<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"680\" height=\"263\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/congruent-triangles.png\" alt=\"congruent triangles\" class=\"wp-image-41564\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/congruent-triangles.png 680w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/congruent-triangles-300x116.png 300w\" sizes=\"auto, (max-width: 680px) 100vw, 680px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">A triangle has 3 sides and 3 angles,so for triangles to be congruent all 3 sides and angles should be congruent.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We observe that:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Side AC = EG, AB = EF and BC = FG,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">and \u2220 A = \u2220 E, \u2220 B = \u2220 F and \u2220 C = \u2220 G<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, ABC &nbsp;<strong>\u2245 <\/strong>&nbsp;EFG.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">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),&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-difference-between-congruent-figures-and-similar-figures\">Difference between Congruent Figures and Similar Figures<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The significant difference between congruent figures and similar figures is that:&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-regular eplus-wrapper\"><table class=\"wj-table-class\"><thead><tr><th><strong>Congruent Figures<\/strong><\/th><th><strong>Similar Figures<\/strong><\/th><\/tr><\/thead><tbody><tr><td>In two congruent figures, both the corresponding angles and the lengths of the corresponding sides are equal to each other.<\/td><td>In two similar figures, the shapes look the same. This is because the corresponding angles are equal. However, the lengths of the corresponding sides are not equal to each other.&nbsp;<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"680\" height=\"571\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/difference-between-congruent-figures-and-similar-figures.png\" alt=\"Difference between Congruent Figures and Similar Figures\" class=\"wp-image-41565\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/difference-between-congruent-figures-and-similar-figures.png 680w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/difference-between-congruent-figures-and-similar-figures-300x252.png 300w\" sizes=\"auto, (max-width: 680px) 100vw, 680px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">As per the above diagram, Congruent Figures are represented by ABC and DEF, whereas Similar Figures are represented by MNO and XYZ&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">In regards to Congruent Figures,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Side AC = DF, AB = DE and BC = EF,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">\u2220 A = \u2220 D, \u2220 B = \u2220 E and \u2220 C = \u2220 F<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, ABC <strong>\u2245<\/strong> &nbsp;DEF, as both the corresponding angles and the lengths of the corresponding side are equal to each other.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Whereas, with respect to Similar Figures.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Only the angles are equal to each other, which are \u2220 M = \u2220 X, \u2220 N = \u2220 Y and \u2220 O = \u2220 Z.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The length of the corresponding sides are not equal to each other.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, MNO and XYZ are similar to each other.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">However, they are not congruent to each other.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-solved-examples\">Solved Examples<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 1: Are the two angles <\/strong><strong>\u2220 ABC and \u2220 XYZ congruent to each other?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"680\" height=\"263\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/solved-example-congruent-angles.png\" alt=\"Solved Example Congruent Angles\" class=\"wp-image-41566\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/solved-example-congruent-angles.png 680w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/solved-example-congruent-angles-300x116.png 300w\" sizes=\"auto, (max-width: 680px) 100vw, 680px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The measure of \u2220 ABC = 40\u00b0 and \u2220 XYZ = 60\u00b0.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">As per the rule, two angles are congruent if the measures of both the angles are equal to each other.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Measure of &nbsp;\u2220 ABC is not equal to measure of&nbsp; \u2220 XYZ.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore,&nbsp; \u2220 ABC is not congruent to&nbsp; \u2220 XYZ.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 2: <\/strong>Two triangles MNO and XYZ are congruent. Mention the corresponding sides and angles that will be equal.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"680\" height=\"263\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/solved-example-congruent-triangles.png\" alt=\"Solved Example Congruent Triangles\" class=\"wp-image-41567\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/solved-example-congruent-triangles.png 680w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/solved-example-congruent-triangles-300x116.png 300w\" sizes=\"auto, (max-width: 680px) 100vw, 680px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Given, \u2206MNO \u2245 \u2206XYZ&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">As per CPCT,&nbsp; 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 class=\"eplus-wrapper\">Therefore,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">MN = XY<\/p>\n\n\n\n<p class=\"eplus-wrapper\">NO = YZ&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">MO = XZ&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Also,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">\u2220 M = \u2220 X, \u2220 N = \u2220 Y and \u2220 O = \u2220 Z<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 3: Are the below figures similar or congruent to each other?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"680\" height=\"263\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/congruent-circles-1.png\" alt=\"two circle\" class=\"wp-image-41568\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/congruent-circles-1.png 680w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/congruent-circles-1-300x116.png 300w\" sizes=\"auto, (max-width: 680px) 100vw, 680px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">In the above diagram, the length of the radius OL is equal to 2 cm, whereas OM is equal to 1 cm.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For two circles to be congruent to each other, the length of the radius of both the circles should be equal to each other.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, both the circles are similar to each other, but they are not congruent to each other.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Conclusion<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">We understand that identical shapes and sizes are called congruent in <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/geometry\" title=\"\">geometry<\/a>. In congruent figures, the shape and size should remain equal when we flip, turn or even rotate the shapes. And in congruent shape, two figures can be placed over each other.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">With SplashLearn, your child can learn about this chapter with solved examples in an exciting way. To strengthen your child\u2019s basics in mathematics, SplashLearn is the best and most trusted platform for every kid. This online educational platform makes learning easy and engaging for your child.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>CTA<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Are you looking for an online educational platform that is entertaining and educational at the same time? Do you want your child to learn and practice mathematics while having fun? Then, don\u2019t wait too long!&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Sign up for <a href=\"https:\/\/www.splashlearn.com\/features\/parents\">SplashLearn <\/a>and boost your child\u2019s confidence in learning mathematics.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-practice-problems\">Practice Problems<\/h2>\n\n\n\n<figure class=\"wp-block-table is-style-regular eplus-wrapper\"><table class=\"wj-table-class\"><tbody><tr><td><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Congruent<\/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\">Find out the false answer in the case of two congruent figures.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Congruent figures are equal in size<\/div><div class=\"spq_answer_block\" data-value=\"1\">Congruent figures can be overlapped<\/div><div class=\"spq_answer_block\" data-value=\"2\">Congruent figures are not equal in shape<\/div><div class=\"spq_answer_block\" data-value=\"3\">Congruent figures can be rotated<\/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 figures are not equal in shape<br\/>The answer is III. Congruent figures are equal in shape too.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">In the case of two congruent triangles \u25b3ABC and \u25b3MNO, if angle A is 55\u00b0, what is the measure of angle M when it corresponds to angle A?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">65\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"1\">55\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"2\">40\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"3\">None 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: 55\u00b0<br\/>The answer is II, 55\u00b0. In the case of two congruent triangles, corresponding angles are equal. \u25b3ABC and \u25b3MNO, if angle A is 55\u00b0, angle M will also be 55\u00b0.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">If \u25b3ABC \u2245 \u25b3PQR, then which angle will be congruent to\u2220 R?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">\u2220B<\/div><div class=\"spq_answer_block\" data-value=\"1\">\u2220C<\/div><div class=\"spq_answer_block\" data-value=\"2\">\u2220A<\/div><div class=\"spq_answer_block\" data-value=\"3\">None 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: \u2220C<br\/>The correct answer is II. If \u25b3ABC \u2245 \u25b3PQR, then angle C will be congruent to corresponding angle R.<\/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\": \"Congruent\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Congruent\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find out the false answer in the case of two congruent figures.\",\n                    \"text\": \"Find out the false answer in the case of two congruent figures.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The answer is III. Congruent figures are equal in shape too.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Congruent figures are equal in size\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The answer is III. Congruent figures are equal in shape too.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Congruent figures can be overlapped\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The answer is III. Congruent figures are equal in shape too.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Congruent figures can be rotated\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The answer is III. Congruent figures are equal in shape too.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Congruent figures are not equal in shape\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The answer is III. Congruent figures are equal in shape too.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The answer is III. Congruent figures are equal in shape too.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"In the case of two congruent triangles \u25b3ABC and \u25b3MNO, if angle A is 55\u00b0, what is the measure of angle M when it corresponds to angle A?\",\n                    \"text\": \"In the case of two congruent triangles \u25b3ABC and \u25b3MNO, if angle A is 55\u00b0, what is the measure of angle M when it corresponds to angle A?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The answer is II, 55\u00b0. In the case of two congruent triangles, corresponding angles are equal. \u25b3ABC and \u25b3MNO, if angle A is 55\u00b0, angle M will also be 55\u00b0.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"65\u00b0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The answer is II, 55\u00b0. In the case of two congruent triangles, corresponding angles are equal. \u25b3ABC and \u25b3MNO, if angle A is 55\u00b0, angle M will also be 55\u00b0.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"40\u00b0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The answer is II, 55\u00b0. In the case of two congruent triangles, corresponding angles are equal. \u25b3ABC and \u25b3MNO, if angle A is 55\u00b0, angle M will also be 55\u00b0.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above \",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The answer is II, 55\u00b0. In the case of two congruent triangles, corresponding angles are equal. \u25b3ABC and \u25b3MNO, if angle A is 55\u00b0, angle M will also be 55\u00b0.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"55\u00b0\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The answer is II, 55\u00b0. In the case of two congruent triangles, corresponding angles are equal. \u25b3ABC and \u25b3MNO, if angle A is 55\u00b0, angle M will also be 55\u00b0.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The answer is II, 55\u00b0. In the case of two congruent triangles, corresponding angles are equal. \u25b3ABC and \u25b3MNO, if angle A is 55\u00b0, angle M will also be 55\u00b0.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If \u25b3ABC \u2245 \u25b3PQR, then which angle will be congruent to\u2220 R?\",\n                    \"text\": \"If \u25b3ABC \u2245 \u25b3PQR, then which angle will be congruent to\u2220 R?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The correct answer is II. If \u25b3ABC \u2245 \u25b3PQR, then angle C will be congruent to corresponding angle R.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"\u2220B\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The correct answer is II. If \u25b3ABC \u2245 \u25b3PQR, then angle C will be congruent to corresponding angle R.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"\u2220A\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The correct answer is II. If \u25b3ABC \u2245 \u25b3PQR, then angle C will be congruent to corresponding angle R.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above \",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The correct answer is II. If \u25b3ABC \u2245 \u25b3PQR, then angle C will be congruent to corresponding angle R.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"\u2220C\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The correct answer is II. If \u25b3ABC \u2245 \u25b3PQR, then angle C will be congruent to corresponding angle R.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The correct answer is II. If \u25b3ABC \u2245 \u25b3PQR, then angle C will be congruent to corresponding angle R.\"\n                      }\n                    } \n\n                    }]}<\/script><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-bd70c9c0-e5e7-4b43-a9d0-806e43d0d61c\" 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-bd70c9c0-e5e7-4b43-a9d0-806e43d0d61c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-bd70c9c0-e5e7-4b43-a9d0-806e43d0d61c\"><strong>When can we say two figures are 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-bd70c9c0-e5e7-4b43-a9d0-806e43d0d61c\">\n\n<p>Two figures can be called congruent when they are of the same shape and the same size.<\/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-bd70c9c0-e5e7-4b43-a9d0-806e43d0d61c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-bd70c9c0-e5e7-4b43-a9d0-806e43d0d61c\"><strong>Can congruent shapes be of different sizes?<\/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-bd70c9c0-e5e7-4b43-a9d0-806e43d0d61c\">\n\n<p>No, congruent figures cannot have different sizes. Instead, the figures are termed to be congruent if they have the same shape and same size. Figures with same shape and different sizes are said to similar.<\/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-bd70c9c0-e5e7-4b43-a9d0-806e43d0d61c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-bd70c9c0-e5e7-4b43-a9d0-806e43d0d61c\"><strong>Are all congruent figures similar?<\/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-bd70c9c0-e5e7-4b43-a9d0-806e43d0d61c\">\n\n<p>Yes, all congruent figures are similar.<\/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-bd70c9c0-e5e7-4b43-a9d0-806e43d0d61c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-bd70c9c0-e5e7-4b43-a9d0-806e43d0d61c\"><strong>Can congruent shapes or figures be mirror images?<\/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-bd70c9c0-e5e7-4b43-a9d0-806e43d0d61c\">\n\n<p>Yes, Congruent figures can be considered as mirror images as they have the same shape and same size.&nbsp;<\/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-bd70c9c0-e5e7-4b43-a9d0-806e43d0d61c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-bd70c9c0-e5e7-4b43-a9d0-806e43d0d61c\"><strong>Do congruent circles have the same diameter?<\/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-bd70c9c0-e5e7-4b43-a9d0-806e43d0d61c\">\n\n<p>Two circles are known to be congruent if their radius is equal to each other. The length of a diameter is twice the radius. Therefore, congruent circles have the same diameter.&nbsp;<\/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-5-bd70c9c0-e5e7-4b43-a9d0-806e43d0d61c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-bd70c9c0-e5e7-4b43-a9d0-806e43d0d61c\"><strong>Can stars 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-5-bd70c9c0-e5e7-4b43-a9d0-806e43d0d61c\">\n\n<p>Two stars can only be considered congruent if both of them have the same shape and size, even when flipped, rotated or overlapped onto each other.&nbsp;<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Meaning of Congruent If two figures can be placed precisely over each other, they are said to be \u2018congruent\u2019 figures. If you place one slice of bread over the other, you will find that both the slices are of equal shape and size.&nbsp; The term \u201ccongruent\u201d means exactly equal shape and size. This shape and &#8230; <a title=\"Congruent &#8211; Definition with Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/congruent\" aria-label=\"More on Congruent &#8211; Definition with Examples\">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-1506","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\/1506","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=1506"}],"version-history":[{"count":10,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1506\/revisions"}],"predecessor-version":[{"id":41569,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1506\/revisions\/41569"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=1506"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=1506"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=1506"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}