{"id":155664,"date":"2022-03-26T00:53:50","date_gmt":"2022-03-25T19:23:50","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/area-of-similar-triangles-properties-formulas-and-solved-examples\/"},"modified":"2023-01-02T12:48:23","modified_gmt":"2023-01-02T07:18:23","slug":"area-of-similar-triangles-properties-formulas-and-solved-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/area-of-similar-triangles\/","title":{"rendered":"Area of Similar Triangles &#8211; Properties, Formulas and Solved Examples"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/area-of-similar-triangles\/#Area_of_Two_Similar_Triangles\" title=\"Area of Two Similar Triangles\">Area of Two Similar Triangles<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/area-of-similar-triangles\/#Properties_of_Area_of_Similar_Triangles\" title=\"Properties of Area of Similar Triangles\">Properties of Area of Similar Triangles<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/area-of-similar-triangles\/#Formulas_of_Area_of_Similar_Triangles\" title=\"Formulas of Area of Similar Triangles\">Formulas of Area of Similar Triangles<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/area-of-similar-triangles\/#Similar_Triangles_and_Congruent_Triangles\" title=\"Similar Triangles and Congruent Triangles\">Similar Triangles and Congruent Triangles<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/area-of-similar-triangles\/#1_Angle-Angle_Similarity_or_AAA\" title=\"1. Angle-Angle Similarity or (AAA)\">1. Angle-Angle Similarity or (AAA)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/area-of-similar-triangles\/#2_Side-Side-Side_Similarity_SSS\" title=\"2. Side-Side-Side Similarity (SSS)\">2. Side-Side-Side Similarity (SSS)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/area-of-similar-triangles\/#3_Side-Angle-Side_Similarity_or_SAS\" title=\"3. Side-Angle-Side Similarity or (SAS)\">3. Side-Angle-Side Similarity or (SAS)<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Area_of_Two_Similar_Triangles\"><\/span>Area of Two Similar Triangles<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The area of two similar triangles is equal to the product of the corresponding sides of the triangles divided by the square of the sine of the angle of similarity.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-155663 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/area-of-similar-triangles-properties-formulas-and-solved-examples.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/area-of-similar-triangles-properties-formulas-and-solved-examples.jpg?v=1648236227 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/area-of-similar-triangles-properties-formulas-and-solved-examples-300x212.jpg?v=1648236227 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Properties_of_Area_of_Similar_Triangles\"><\/span>Properties of Area of Similar Triangles<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The properties of the area of similar triangles are that the areas of the triangles are proportional to the squares of the corresponding sides. This means that if two triangles are similar, then the ratio of the areas of the two triangles is the same as the ratio of the corresponding sides. Additionally, the area of a triangle is found by multiplying the base by the height and dividing by two.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Formulas_of_Area_of_Similar_Triangles\"><\/span>Formulas of Area of Similar Triangles<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The area of a triangle can be found using the following formula:<\/p>\n<p>A = b x h<\/p>\n<p>Where b is the base of the triangle and h is the height.<\/p>\n<p>The area of a triangle is also equal to one-half the base multiplied by the height.<\/p>\n<p>A = 1\/2 b x h<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Similar_Triangles_and_Congruent_Triangles\"><\/span>Similar Triangles and Congruent Triangles<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A triangle is congruent to another triangle if and only if the three angles of the first triangle are congruent to the three angles of the second triangle.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"1_Angle-Angle_Similarity_or_AAA\"><\/span>1. Angle-Angle Similarity or (AAA)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Theorem: If two angles are congruent, then they are also similar.<\/p>\n<p>Proof:<\/p>\n<p>Angles are congruent if and only if they have the same measure. We can see that if two angles are similar, then they must have the same measure because the angles are formed by the same lines and the ratios of the corresponding sides are the same.<\/p>\n<p>\\begin{align*}\\angle A&amp;=\\angle B\\\\ \\frac{AB}{BC}&amp;=\\frac{BA}{CA}\\\\ \\angle A&amp;=\\angle B\\\\ \\)\\end{align*} Angle A=Angle B<br \/>\n\\\\\\frac{AB}{BC}=\\frac{BA}{CA}\\\\\\angle A=\\angle B\\\\<\/p>\n<p>Since the angles are congruent and the corresponding ratios of the sides are the same, it follows that the angles are also similar.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"2_Side-Side-Side_Similarity_SSS\"><\/span>2. Side-Side-Side Similarity (SSS)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>SSS similarity is the similarity between three objects that are placed in a line next to each other. The objects are usually aligned so that their corresponding sides are parallel to each other.<\/p>\n<p>In the image below, the three squares are similar because their corresponding sides are parallel to each other. The top and bottom squares are also similar because their corresponding sides are perpendicular to each other.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"3_Side-Angle-Side_Similarity_or_SAS\"><\/span>3. Side-Angle-Side Similarity or (SAS)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The Side-Angle-Side Similarity postulate states that two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Area of Two Similar Triangles The area of two similar triangles is equal to the product of the corresponding sides [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Area of Similar Triangles","_yoast_wpseo_title":"Area of Similar Triangles - Properties, Formulas and Solved Examples","_yoast_wpseo_metadesc":"Learn about area of similar triangles topic of Maths in details explained by subject experts on infinitylearn.com. 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