{"id":32898,"date":"2023-08-13T16:50:02","date_gmt":"2023-08-13T16:50:02","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=32898"},"modified":"2023-08-13T18:00:55","modified_gmt":"2023-08-13T18:00:55","slug":"sas-side-angle-side-theorem-definition-congruence-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/sas","title":{"rendered":"SAS (Side Angle Side) Theorem | Definition, Congruence, Examples"},"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-a342ff48-42a3-4cbc-952d-2fd6e77ac1ab\" 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\/sas#0-what-is-sas-theorem-side-angle-side-theorem-in-geometry>What Is SAS Theorem (Side-Angle-Side Theorem) in Geometry?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/sas#2-sas-side-angle-side-congruence-theorem>SAS (Side-Angle-Side) Congruence Theorem<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/sas#3-sas-side-angle-side-similarity-rule>SAS (Side-Angle-Side) Similarity Rule<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/sas#6-solved-examples-on%C2%A0-sas-theorem>Solved Examples on\u00a0 SAS Theorem<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/sas#7-practice-problems-on-sas-theorem>Practice Problems on SAS Theorem<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/sas#8-frequently-asked-questions-on%C2%A0-sas-theorem>Frequently Asked Questions on\u00a0 SAS Theorem<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-sas-theorem-side-angle-side-theorem-in-geometry\">What Is SAS Theorem (Side-Angle-Side Theorem) in Geometry?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>The SAS theorem, which stands for Side-Angle-Side theorem, is a criterion used to prove triangle congruence and also triangle similarity.<\/strong> However, the terms or the conditions of the SAS theorem for triangle congruence and triangle similarity are slightly different.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Congruent Triangles: <\/strong>Two <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/triangle\">triangles<\/a> are said to be <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/congruent\">congruent<\/a> if they have the same shape and the same size. Corresponding angles and corresponding sides of two congruent triangles are also congruent. The triangle congruence is denoted using the symbol \u2245.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Similar Triangles:<\/strong> Two triangles are said to be similar if they have the same shape but different sizes. Corresponding angles of similar triangles are congruent. Corresponding sides of two similar triangles are proportional. We denote the triangle similarity using the symbol .<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The SAS theorem helps to prove the triangle congruence (or similarity) based on the lengths of any two sides and the measurement of the included angle between these sides.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"1-sas-definition-in-geometry\">SAS Definition in Geometry<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>SAS Congruence Theorem:<\/strong> When the two sides of a triangle are equal to the two sides of another triangle, and the angles formed by these sides (the included angles) are also equal, then the two triangles are congruent.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"533\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/sas-congruence-theorem.png\" alt=\"SAS Congruence theorem\" class=\"wp-image-32945\" title=\"SAS Congruence theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/sas-congruence-theorem.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/sas-congruence-theorem-300x258.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>SAS Similarity Criterion: <\/strong>If two sides of a triangle are proportional with two sides of another triangle, and if the corresponding included angles formed by these sides are congruent, then the two triangles are similar.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"346\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/sas-similarity-theorem.png\" alt=\"SAS similarity theorem\" class=\"wp-image-32947\" title=\"SAS similarity theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/sas-similarity-theorem.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/sas-similarity-theorem-300x167.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"2-sas-side-angle-side-congruence-theorem\">SAS (Side-Angle-Side) Congruence Theorem<\/h2>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-d533ae86-11aa-4f66-8d45-962a1c393382\">\n\n\n<p class=\"wp-block-paragraph\"><strong>SAS congruence theorem<\/strong> states that, if two sides and the included angle of one triangle are congruent to the two sides and the included angle of another triangle, then the triangles are congruent.<\/p>\n\n\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><strong>SSS Congruence Theorem Example:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Are the given two triangles congruent?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"278\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/sas-congruence-theorem-example.png\" alt=\"SAS congruence theorem - example\" class=\"wp-image-32948\" title=\"SAS congruence theorem - example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/sas-congruence-theorem-example.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/sas-congruence-theorem-example-300x135.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">AB= EF = 7        units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">BC = DE = 5         units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2220B= \u2220E = $50^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus,&nbsp; \u0394ABC \u2245 \u0394FED by SAS congruence theorem<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-sas-side-angle-side-similarity-rule\">SAS (Side-Angle-Side) Similarity Rule<\/h2>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-5baa5f28-ff64-4a14-81af-29800a7235e5\">\n\n\n<p class=\"wp-block-paragraph\">SAS congruence theorem states that, if two sides of one triangle are proportional to the corresponding sides of another triangle, and if the corresponding included angles are also equal, then the triangles are similar.<\/p>\n\n\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><strong>SAS Similarity Theorem Example:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Are the two triangles similar?<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"512\" height=\"260\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/sas-similarity-criterion.png\" alt=\"SAS Similarity Criterion\" class=\"wp-image-32949\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/sas-similarity-criterion.png 512w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/sas-similarity-criterion-300x152.png 300w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Here,&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\frac{ML}{RQ} = \\frac{LN}{QS} = \\frac{1}{2}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">m\u2220 L = m\u2220 Q $= 80^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">By SAS similarity rule, \u0394MLN \u2245 \u0394QRS<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-facts-about-sas-theorem\">Facts about SAS theorem<\/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-4fc3f8e1 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>SAS theorem is applicable to all types of triangles as long as the conditions of the SAS rule are satisfied.&nbsp;<\/li>\n\n\n\n<li>The positions of letters in SAS are significant. It refers to the combination of sides and angles used to prove the congruence or similarity. Since the angle A lies between two sides (S), we use the term \u201cincluded angle.\u201d<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In this article, we learned about the SAS theorem for both congruence and similarity rule <strong>examples. <\/strong>Now let us practice solving problems on the SAS Theorem.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-solved-examples-on%C2%A0-sas-theorem\">Solved Examples on\u00a0 SAS Theorem<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. Are triangles ABC and BCD similar?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"264\" height=\"203\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/proving-triangle-similarity-by-sas-rule.png\" alt=\"Proving triangle similarity by SAS rule\" class=\"wp-image-32951\" title=\"Proving triangle similarity by SAS rule\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In \u0394ABC and \u0394BCD,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\frac{AB}{BD} = \\frac{27}{18} = \\frac{3}{2}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\frac{EB}{BC} = \\frac{36}{24} = \\frac{3}{2}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, $\\frac{AB}{BD} = \\frac{EB}{BC}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Also, \u2220ABE = \u2220CBD (vertical angles)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, \u0394ABC~ \u0394BCD by SAS similarity rule<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. Prove that <\/strong>\u0394YXZ \u2245 \u0394SRT.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"280\" height=\"188\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/proving-triangle-congruence-by-sas-rule.png\" alt=\"Proving triangle congruence by SAS rule\" class=\"wp-image-32952\" title=\"Proving triangle congruence by SAS rule\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">XY = RS = 5 in<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">XZ = RT = 8.5 in&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2220YXZ is the included angle between XY and XZ.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2220SRT is the included angle between SR and RT.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2220YXZ = \u2220SRT = 60\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, by SAS congruence rule, \u0394YXZ \u2245 \u0394SRT.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>3. Prove that <\/strong>\u0394ABC \u2245 \u0394CDA.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"288\" height=\"153\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/sas-triangle-congruence-example.png\" alt=\"SAS triangle congruence example\" class=\"wp-image-32954\" title=\"SAS triangle congruence example\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">BC = AD (given)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">AC = AC (common side)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">BC || AD (given)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2220DAC = \u2220BCA (Alternate angles formed by a transversal cutting two parallel lines)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2220DAC is included angle between AC and AD.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2220BCA is included angle between BC and AC.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, <strong>\u00a0<\/strong>\u0394ABC \u2245 \u0394CDA                                      By SAS congruence rule.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-practice-problems-on-sas-theorem\">Practice Problems on SAS Theorem<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">SAS (Side Angle Side) Theorem | Definition, Congruence, Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">What is the full form of the SAS theorem?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Side-Angle-Side<\/div><div class=\"spq_answer_block\" data-value=\"1\">Angle-Side-Angle<\/div><div class=\"spq_answer_block\" data-value=\"2\">Side-Side-Side<\/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: Side-Angle-Side<br\/>SAS stands for Side-Angle-Side.<\/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\">In SAS theorem, the angle A refers to<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">any interior angle<\/div><div class=\"spq_answer_block\" data-value=\"1\">angle<\/div><div class=\"spq_answer_block\" data-value=\"2\">the included angle<\/div><div class=\"spq_answer_block\" data-value=\"3\">Non-included angle<\/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: the included angle<br\/>In SAS theorem, A is the angle included between the given two sides.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Which of the following measurements of sides and angles are required to prove congruence using the SAS theorem?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Two sides and the non-included angle<\/div><div class=\"spq_answer_block\" data-value=\"1\">Two angles and the non-included side<\/div><div class=\"spq_answer_block\" data-value=\"2\">Two sides and the included angle<\/div><div class=\"spq_answer_block\" data-value=\"3\">Two angles and the included angle<\/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: Two sides and the included angle<br\/>To prove that two triangles are congruent by SAS rule, two sides and the included angle of a triangle must be congruent to two sides and included angle of another triangle.<\/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\": \"SAS (Side Angle Side) Theorem | Definition, Congruence, Examples\",    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\"To prove that two triangles are congruent by SAS rule, two sides and the included angle of a triangle must be congruent to two sides and included angle of another triangle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Two angles and the included angle\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"To prove that two triangles are congruent by SAS rule, two sides and the included angle of a triangle must be congruent to two sides and included angle of another triangle.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Two sides and the included angle\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"To prove that two triangles are congruent by SAS rule, two sides and the included angle of a triangle must be congruent to two sides and included angle of another triangle.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"To prove that two triangles are congruent by SAS rule, two sides and the included angle of a triangle must be congruent to two sides and included angle of another triangle.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-frequently-asked-questions-on%C2%A0-sas-theorem\">Frequently Asked Questions on\u00a0 SAS Theorem<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-6f2df8d9-c3df-4ddc-9bd6-a1ed4f2c2b9c\" 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-0-6f2df8d9-c3df-4ddc-9bd6-a1ed4f2c2b9c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6f2df8d9-c3df-4ddc-9bd6-a1ed4f2c2b9c\"><strong>What is the difference between SAS congruence rule and ASA 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-0-6f2df8d9-c3df-4ddc-9bd6-a1ed4f2c2b9c\">\n\n<p class=\"wp-block-paragraph\">We apply the SAS rule when two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle. The ASA congruence rule is used when two angles and the included side of one triangle are congruent to the two angles and the included side of another 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-1-6f2df8d9-c3df-4ddc-9bd6-a1ed4f2c2b9c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6f2df8d9-c3df-4ddc-9bd6-a1ed4f2c2b9c\"><strong>What is the difference between SAS and SSS rules?<\/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-1-6f2df8d9-c3df-4ddc-9bd6-a1ed4f2c2b9c\">\n\n<p class=\"wp-block-paragraph\">SAS stands for \u201cSide-Angle-Side\u201d and SSS stands for \u201cSide-Side-Side.\u201d Both rules are the triangle congruence rules.<\/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-2-6f2df8d9-c3df-4ddc-9bd6-a1ed4f2c2b9c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6f2df8d9-c3df-4ddc-9bd6-a1ed4f2c2b9c\"><strong>Can the SAS theorem be used to prove similarity of 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-2-6f2df8d9-c3df-4ddc-9bd6-a1ed4f2c2b9c\">\n\n<p class=\"wp-block-paragraph\">Yes, SAS is the criterion in both triangle congruence and triangle similarity theorems.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is SAS Theorem (Side-Angle-Side Theorem) in Geometry? The SAS theorem, which stands for Side-Angle-Side theorem, is a criterion used to prove triangle congruence and also triangle similarity. However, the terms or the conditions of the SAS theorem for triangle congruence and triangle similarity are slightly different. Congruent Triangles: Two triangles are said to be &#8230; <a title=\"SAS (Side Angle Side) Theorem | Definition, Congruence, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/sas\" aria-label=\"More on SAS (Side Angle Side) Theorem | Definition, Congruence, 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-32898","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\/32898","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=32898"}],"version-history":[{"count":8,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/32898\/revisions"}],"predecessor-version":[{"id":32957,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/32898\/revisions\/32957"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=32898"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=32898"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=32898"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}