{"id":35050,"date":"2023-10-16T15:15:55","date_gmt":"2023-10-16T15:15:55","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=35050"},"modified":"2023-10-16T15:43:33","modified_gmt":"2023-10-16T15:43:33","slug":"rhs-congruence-rule-statement-proof-examples-facts-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/rhs","title":{"rendered":"RHS Congruence Rule &#8211; Statement, Proof, Examples, Facts, 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-4d1595ad-92d2-42c5-80ed-d2709f090579\" 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\/rhs#0-what-is-the-rhs-congruence-rule-in-geometry>What Is the RHS Congruence Rule in Geometry?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/rhs#1-rhs-congruence-rule-statement>RHS Congruence Rule Statement<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/rhs#2-proof-of-rhs-congruence-theorem>Proof of RHS Congruence Theorem<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/rhs#5-solved-examples-on-rhs-congruence-theorem>Solved Examples on RHS Congruence Theorem<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/rhs#6-practice-problems-on-rhs-congruence-theorem>Practice Problems on RHS Congruence Theorem<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/rhs#7-frequently-asked-questions-about-rhs-congruence-theorem>Frequently Asked Questions about RHS Congruence Theorem<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-rhs-congruence-rule-in-geometry\">What Is the RHS Congruence Rule in Geometry?<\/h2>\n\n\n\n<p><strong>RHS (Right angle-Hypotenuse-Side) congruence criterion is used to prove the congruence of two <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/right-triangle\"><strong>right-angled triangles<\/strong><\/a><strong>.<\/strong> It states that if the hypotenuse and one side (leg) of one right triangle are <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/congruent\">congruent<\/a> to the hypotenuse and the corresponding side of the other right triangle, then the two right triangles are congruent.<\/p>\n\n\n\n<p>In the diagram shown below, there are two right triangles \u25b5ABC &amp;&nbsp; \u25b5PQR such that&nbsp;<\/p>\n\n\n\n<p>hypotenuse AC = hypotenuse PR<\/p>\n\n\n\n<p>Side AB = Side PQ<\/p>\n\n\n\n<p>Thus, by RHS congruence criterion, \u25b5ABC \u2245&nbsp; \u25b5PQR<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"347\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/rhs-right-angle-hypotenuse-side-congruence-rule.png\" alt=\"RHS (Right angle-Hypotenuse-Side) Congruence Rule\" class=\"wp-image-35054\" title=\"RHS (Right angle-Hypotenuse-Side) Congruence Rule\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/rhs-right-angle-hypotenuse-side-congruence-rule.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/rhs-right-angle-hypotenuse-side-congruence-rule-300x168.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>The RHS congruence rule is also known as the HL (Hypotenuse-Leg) congruence rule. Note that this theorem is only applicable to the right-angled triangles.<\/p>\n\n\n\n<p>The RHS rule is based on the Pythagoras theorem. In a right triangle, if we know the length of any two sides, we can find the length of the missing side using the Pythagoras theorem, which states that&nbsp;<\/p>\n\n\n\n<p><strong>Hypotenuse<\/strong><strong><sup>2<\/sup><\/strong><strong> = Base<\/strong><strong><sup>2 <\/sup><\/strong><strong>+ Perpendicular<\/strong><strong><sup>2<\/sup><\/strong><\/p>\n\n\n\n<p>Thus, if the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/hypotenuse\">hypotenuse<\/a> and one side of one right triangle are congruent to the hypotenuse and corresponding side of another right triangle, the remaining sides will automatically be equal.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"1-rhs-congruence-rule-statement\">RHS Congruence Rule Statement<\/h2>\n\n\n\n<p>The RHS (Right Angle-Hypotenuse-Side) congruence rule states that if the hypotenuse and one side of one right triangle is equal to the hypotenuse and corresponding side of the other right triangle, then the two given right triangles are congruent.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"2-proof-of-rhs-congruence-theorem\">Proof of RHS Congruence Theorem<\/h2>\n\n\n\n<p><strong>Given:<\/strong> Two right-angled triangles ABC and&nbsp; DEF where \u2220B=90\u00b0&nbsp; and \u2220E=90\u00b0.<\/p>\n\n\n\n<p>Hypotenuses are equal. (AC = DF)<\/p>\n\n\n\n<p>One pair of corresponding sides is equal. (BC = EF)<\/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\/10\/two-right-triangles-angle-abc-and-angle-def.png\" alt=\"Two right triangles - \u25b5ABC and \u25b5DEF\" class=\"wp-image-35056\" title=\"Two right triangles - \u25b5ABC and \u25b5DEF\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/two-right-triangles-angle-abc-and-angle-def.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/two-right-triangles-angle-abc-and-angle-def-300x172.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>To prove: <\/strong>\u0394ABC \u2245 \u0394DEF<\/p>\n\n\n\n<p><strong>Proof:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\"><strong><strong>Statement<\/strong><\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Reason<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">$AC^{2} = AB^{2} + BC^{2}$<br>$\\Rightarrow AB^{2} = AC^{2} &#8211; BC^{2}$ \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026(1)<\/td><td class=\"has-text-align-left\" data-align=\"left\">Pythagoras theorem in right triangle ABC<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">$DF^{2} = DE^{2} + EF^{2}$<br>$\\Rightarrow DE^{2} = DF^{2} &#8211; EF^{2}$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026(2)<\/td><td class=\"has-text-align-left\" data-align=\"left\">Pythagoras theorem in right triangle DEF<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">AC = DF and BC = EF\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026(3)<\/td><td class=\"has-text-align-left\" data-align=\"left\">Given<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">$AB^{2} = DF^{2} &#8211; EF^{2}$ \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026(4)<\/td><td class=\"has-text-align-left\" data-align=\"left\">From (1) and (3)<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">$AB^{2} = DE^{2}$<br>$\\Rightarrow AB = DE$<\/td><td class=\"has-text-align-left\" data-align=\"left\">From (2) and (4)<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">In \u0394ABC and\u00a0 \u0394DEF,<br>AB = DE<br>BC = EF<br>AC = DF<\/td><td class=\"has-text-align-left\" data-align=\"left\">From (3) and (4)<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\u0394ABC \u2245 \u0394DEF<\/td><td class=\"has-text-align-left\" data-align=\"left\">SSS Congruence Criterion<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about the Right Hand Side (RHS) Congruence Rule and how it is applied. By understanding this rule, we can determine the congruence of two right triangles based on the congruence of their hypotenuse and one corresponding leg. Let&#8217;s solidify our understanding by working through examples and practicing MCQs for better comprehension.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-facts-about-rhs-congruence-rule\">Facts about RHS Congruence Rule<\/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>The RHS (Right-Hand-Side) Congruence Rule is also known as the Hypotenuse-Leg Congruence Rule or the HL Congruence Rule.<\/li>\n\n\n\n<li>The RHS congruence rule is only applicable to right triangles.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-solved-examples-on-rhs-congruence-theorem\">Solved Examples on RHS Congruence Theorem<\/h2>\n\n\n\n<p><strong>Example 1: In the given figure PQ = PR, <\/strong><strong>\u2220PSQ=\u2220PSR=90\u00b0<\/strong><strong>. Prove that&nbsp; <\/strong><strong>\u0394PSQ \u2245 \u0394PSR<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"288\" height=\"199\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/RHS-theorem-problem.png\" alt=\"RHS theorem problem\" class=\"wp-image-35058\" title=\"RHS theorem problem\"\/><\/figure>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>In \u0394PSQ and \u0394PSR,<\/p>\n\n\n\n<p>PQ = PR (given)<\/p>\n\n\n\n<p>PS = PS (common side)<\/p>\n\n\n\n<p>\u2220QSP=\u2220RSP (both right angles)<\/p>\n\n\n\n<p>Hypotenuse and one side of \u0394PSQ is congruent to the hypotenuse and the corresponding side of&nbsp; \u0394PSR.<\/p>\n\n\n\n<p>Thus, by RHS rule, \u0394PSQ \u2245 \u0394PSR. Hence proved.&nbsp;<\/p>\n\n\n\n<p><strong>Example 2: Are the two right triangles <\/strong><strong>\u0394ABC<\/strong><strong> and <\/strong><strong>\u0394PQR<\/strong><strong> congruent by RHS rule?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"276\" height=\"153\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/two-right-triangles-abc-and-pqr.png\" alt=\"Two right triangles ABC and PQR\" class=\"wp-image-35060\" title=\"Two right triangles ABC and PQR\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>To prove that two right triangles \u0394ABC and \u0394PQR are congruent by RHS congruence criterion, the hypotenuse and one side of \u0394ABC must be congruent to the hypotenuse and the corresponding side of \u0394PQR.<\/p>\n\n\n\n<p>Here, it is given that AB = QR and \u2220ABC=\u2220PQR=90.&nbsp;<\/p>\n\n\n\n<p>However, it is not mentioned that the hypotenuses are equal.<\/p>\n\n\n\n<p>Thus, we cannot say that the two triangles are congruent by RHS congruence rule. The information is not sufficient.<\/p>\n\n\n\n<p><strong>Example 3: Prove the given triangles are congruent.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"290\" height=\"149\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/proving-triangle-congruence-by-RHS-rule.png\" alt=\"Proving triangle congruence by RHS rule\" class=\"wp-image-35061\" title=\"Proving triangle congruence by RHS rule\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>In the given triangles, <strong>\u0394YXZ<\/strong><strong> <\/strong>and <strong>\u0394PQR<\/strong><strong>,<\/strong><\/p>\n\n\n\n<p>side XZ = side PQ (given)<\/p>\n\n\n\n<p>Hypotenuse YZ = Hypotenuse PR&nbsp; (given)<\/p>\n\n\n\n<p>\u2220<strong>YXZ<\/strong>=\u2220PQR =<strong>90\u00b0<\/strong> (given)<\/p>\n\n\n\n<p>Hypotenuse and one side of \u0394YXZ is congruent to the hypotenuse and the corresponding side of&nbsp; \u0394PQR.<\/p>\n\n\n\n<p>Thus, by RHS theorem, \u0394YXZ \u2245 \u0394PQR.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-practice-problems-on-rhs-congruence-theorem\">Practice Problems on RHS Congruence Theorem<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">RHS Congruence Rule - Statement, Proof, Examples, Facts, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">What does RHS stand for in the RHS congruence theorem?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Right-Hand-Side theorem<\/div><div class=\"spq_answer_block\" data-value=\"1\">Right Angle-Hypotenuse-Side theorem<\/div><div class=\"spq_answer_block\" data-value=\"2\">Right triangle-Hand-Side theorem<\/div><div class=\"spq_answer_block\" data-value=\"3\">Remote angle-Hypotenuse-Side theorem<\/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: Right Angle-Hypotenuse-Side theorem<br\/>The RHS theorem stands for Right side-Hypotenuse-Side theorem.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What information is necessary to prove that \u0394POQ \u2245 \u0394POR by the RHS congruence rule?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">\u2220Q = 2\u2220R<\/div><div class=\"spq_answer_block\" data-value=\"1\">OQ = OR<\/div><div class=\"spq_answer_block\" data-value=\"2\">PQ = PR<\/div><div class=\"spq_answer_block\" data-value=\"3\">\u2220OPQ = \u2220OPR<\/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: PQ = PR<br\/>In \u0394POQ and \u0394POR.<br>\r\nPO = PO  (common side)<br>\r\n\u2220POQ = \u2220POR  = 90\u00b0 (given)<br>\r\nFor \u0394POQ & \u0394POR to be congruent by the RHS rule, the hypotenuses must be congruent.<br>\r\nWe must have PQ = PR.<\/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\">In the right triangle  \u0394ABC, if AB is 4 units and BC is 3 units. Find the side AC.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">25 units<\/div><div class=\"spq_answer_block\" data-value=\"1\">5 units<\/div><div class=\"spq_answer_block\" data-value=\"2\">15 units<\/div><div class=\"spq_answer_block\" data-value=\"3\">10 units<\/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: 5 units<br\/>$Hypotenuse^{2}$ = Base^{2} + Perpendicular^{2}$\t\t\t(by Pythagoras theorem)<br>\r\n$AC^{2} = AB^{2} + BC^{2}$<br>\r\n$AC^{2} = 4^{2} + 3^{2}$<br>\r\n$AC^{2} = 16 + 9$<br>\r\n$AC^{2} = 25$<br>\r\n$AC = \\sqrt{25}$<br>\r\nAC = 5 units<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        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\"@type\": \"Comment\",\n                      \"text\": \"The RHS theorem stands for Right side-Hypotenuse-Side theorem.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Right-Hand-Side theorem\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The RHS theorem stands for Right side-Hypotenuse-Side theorem.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                           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\"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Right Angle-Hypotenuse-Side theorem\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The RHS theorem stands for Right side-Hypotenuse-Side theorem.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The RHS theorem stands for Right side-Hypotenuse-Side theorem.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What information is necessary to prove that \u0394POQ \u2245 \u0394POR by the RHS congruence rule?\",\n                    \"text\": \"What information is necessary to prove that \u0394POQ \u2245 \u0394POR by the RHS congruence rule?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"In \u0394POQ and \u0394POR.<br>\r\nPO = PO  (common side)<br>\r\n\u2220POQ = \u2220POR  = 90\u00b0 (given)<br>\r\nFor \u0394POQ & \u0394POR to be congruent by the RHS rule, the hypotenuses must be congruent.<br>\r\nWe must have PQ = PR.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"\u2220Q = 2\u2220R\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In \u0394POQ and \u0394POR.<br>\r\nPO = PO  (common side)<br>\r\n\u2220POQ = \u2220POR  = 90\u00b0 (given)<br>\r\nFor \u0394POQ & \u0394POR to be congruent by the RHS rule, the hypotenuses must be congruent.<br>\r\nWe must have PQ = PR.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"OQ = OR\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In \u0394POQ and \u0394POR.<br>\r\nPO = PO  (common side)<br>\r\n\u2220POQ = \u2220POR  = 90\u00b0 (given)<br>\r\nFor \u0394POQ & \u0394POR to be congruent by the RHS rule, the hypotenuses must be congruent.<br>\r\nWe must have PQ = PR.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"\u2220OPQ = \u2220OPR\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In \u0394POQ and \u0394POR.<br>\r\nPO = PO  (common side)<br>\r\n\u2220POQ = \u2220POR  = 90\u00b0 (given)<br>\r\nFor \u0394POQ & \u0394POR to be congruent by the RHS rule, the hypotenuses must be congruent.<br>\r\nWe must have PQ = PR.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"PQ = PR\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"In \u0394POQ and \u0394POR.<br>\r\nPO = PO  (common side)<br>\r\n\u2220POQ = \u2220POR  = 90\u00b0 (given)<br>\r\nFor \u0394POQ & \u0394POR to be congruent by the RHS rule, the hypotenuses must be congruent.<br>\r\nWe must have PQ = PR.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"In \u0394POQ and \u0394POR.<br>\r\nPO = PO  (common side)<br>\r\n\u2220POQ = \u2220POR  = 90\u00b0 (given)<br>\r\nFor \u0394POQ & \u0394POR to be congruent by the RHS rule, the hypotenuses must be congruent.<br>\r\nWe must have PQ = PR.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"In the right triangle  \u0394ABC, if AB is 4 units and BC is 3 units. Find the side AC.\",\n                    \"text\": \"In the right triangle  \u0394ABC, if AB is 4 units and BC is 3 units. Find the side AC.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$Hypotenuse^{2}$$ = Base^{2} + Perpendicular^{2}$$\t\t\t(by Pythagoras theorem)<br>\r\n$$AC^{2} = AB^{2} + BC^{2}$$<br>\r\n$$AC^{2} = 4^{2} + 3^{2}$$<br>\r\n$$AC^{2} = 16 + 9$$<br>\r\n$$AC^{2} = 25$$<br>\r\n$$AC = \\\\sqrt{25}$$<br>\r\nAC = 5 units\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"25 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$Hypotenuse^{2}$$ = Base^{2} + Perpendicular^{2}$$\t\t\t(by Pythagoras theorem)<br>\r\n$$AC^{2} = AB^{2} + BC^{2}$$<br>\r\n$$AC^{2} = 4^{2} + 3^{2}$$<br>\r\n$$AC^{2} = 16 + 9$$<br>\r\n$$AC^{2} = 25$$<br>\r\n$$AC = \\\\sqrt{25}$$<br>\r\nAC = 5 units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"15 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$Hypotenuse^{2}$$ = Base^{2} + Perpendicular^{2}$$\t\t\t(by Pythagoras theorem)<br>\r\n$$AC^{2} = AB^{2} + BC^{2}$$<br>\r\n$$AC^{2} = 4^{2} + 3^{2}$$<br>\r\n$$AC^{2} = 16 + 9$$<br>\r\n$$AC^{2} = 25$$<br>\r\n$$AC = \\\\sqrt{25}$$<br>\r\nAC = 5 units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$Hypotenuse^{2}$$ = Base^{2} + Perpendicular^{2}$$\t\t\t(by Pythagoras theorem)<br>\r\n$$AC^{2} = AB^{2} + BC^{2}$$<br>\r\n$$AC^{2} = 4^{2} + 3^{2}$$<br>\r\n$$AC^{2} = 16 + 9$$<br>\r\n$$AC^{2} = 25$$<br>\r\n$$AC = \\\\sqrt{25}$$<br>\r\nAC = 5 units\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"5 units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$Hypotenuse^{2}$$ = Base^{2} + Perpendicular^{2}$$\t\t\t(by Pythagoras theorem)<br>\r\n$$AC^{2} = AB^{2} + BC^{2}$$<br>\r\n$$AC^{2} = 4^{2} + 3^{2}$$<br>\r\n$$AC^{2} = 16 + 9$$<br>\r\n$$AC^{2} = 25$$<br>\r\n$$AC = \\\\sqrt{25}$$<br>\r\nAC = 5 units\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$Hypotenuse^{2}$$ = Base^{2} + Perpendicular^{2}$$\t\t\t(by Pythagoras theorem)<br>\r\n$$AC^{2} = AB^{2} + BC^{2}$$<br>\r\n$$AC^{2} = 4^{2} + 3^{2}$$<br>\r\n$$AC^{2} = 16 + 9$$<br>\r\n$$AC^{2} = 25$$<br>\r\n$$AC = \\\\sqrt{25}$$<br>\r\nAC = 5 units\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-frequently-asked-questions-about-rhs-congruence-theorem\">Frequently Asked Questions about RHS Congruence Theorem<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-2b7059fa-d4c4-4e5c-baf1-5f99f5a22311\" 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-0-2b7059fa-d4c4-4e5c-baf1-5f99f5a22311\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-2b7059fa-d4c4-4e5c-baf1-5f99f5a22311\"><strong>When can we apply the RHS Congruence Rule?<\/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-0-2b7059fa-d4c4-4e5c-baf1-5f99f5a22311\">\n\n<p>The RHS Congruence Rule can be applied when we have to check if two right triangles are congruent, where we know the lengths of the hypotenuse and one side of the triangle.<\/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-1-2b7059fa-d4c4-4e5c-baf1-5f99f5a22311\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-2b7059fa-d4c4-4e5c-baf1-5f99f5a22311\"><strong>Can we use the RHS Congruence Rule to prove congruence for non-right triangles?<\/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-1-2b7059fa-d4c4-4e5c-baf1-5f99f5a22311\">\n\n<p>No, the RHS Congruence Rule is applicable only to the right triangles.<\/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-2-2b7059fa-d4c4-4e5c-baf1-5f99f5a22311\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-2b7059fa-d4c4-4e5c-baf1-5f99f5a22311\"><strong>Is the RHS Congruence rule and the HL congruence theorem same?<\/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-2-2b7059fa-d4c4-4e5c-baf1-5f99f5a22311\">\n\n<p>Yes, the RHS Congruence Rule and the HL (Hypotenuse-Leg) Congruence Theorem are the same.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the RHS Congruence Rule in Geometry? RHS (Right angle-Hypotenuse-Side) congruence criterion is used to prove the congruence of two right-angled triangles. It states that if the hypotenuse and one side (leg) of one right triangle are congruent to the hypotenuse and the corresponding side of the other right triangle, then the two right &#8230; <a title=\"RHS Congruence Rule &#8211; Statement, Proof, Examples, Facts, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/rhs\" aria-label=\"More on RHS Congruence Rule &#8211; Statement, Proof, Examples, Facts, 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-35050","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\/35050","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=35050"}],"version-history":[{"count":8,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/35050\/revisions"}],"predecessor-version":[{"id":35067,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/35050\/revisions\/35067"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=35050"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=35050"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=35050"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}