{"id":155582,"date":"2022-03-26T00:48:20","date_gmt":"2022-03-25T19:18:20","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/introduction-to-angle-sum-triangle-property-proof-and-solved-examples\/"},"modified":"2023-05-12T16:41:38","modified_gmt":"2023-05-12T11:11:38","slug":"introduction-to-angle-sum-triangle-property-proof-and-solved-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/introduction-angle-sum-triangle\/","title":{"rendered":"Introduction to Angle Sum Triangle \u2013 Property, Proof 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\/introduction-angle-sum-triangle\/#Triangle_Sum_Property\" title=\"Triangle Sum Property\">Triangle Sum Property<\/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\/introduction-angle-sum-triangle\/#Angle_Sum_Property_of_a_Triangle\" title=\"Angle Sum Property of a Triangle\">Angle Sum Property of a Triangle<\/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\/introduction-angle-sum-triangle\/#Proof\" title=\"Proof\">Proof<\/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\/introduction-angle-sum-triangle\/#Some_other_Important_Angle_Properties_of_a_Triangle\" title=\"Some other Important Angle Properties of a Triangle\">Some other Important Angle Properties of a Triangle<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Triangle_Sum_Property\"><\/span>Triangle Sum Property<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The Triangle Sum Property states that the sum of the measures of the angles of a triangle is 180 degrees. This is because the angles of a triangle always add up to 180 degrees.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-155581 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/introduction-to-angle-sum-triangle-property-proof-and-solved-examples.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/introduction-to-angle-sum-triangle-property-proof-and-solved-examples.jpg?v=1648235898 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/introduction-to-angle-sum-triangle-property-proof-and-solved-examples-300x212.jpg?v=1648235898 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Angle_Sum_Property_of_a_Triangle\"><\/span>Angle Sum Property of a Triangle<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The angle sum property of a triangle states that the sum of the angles in a triangle is 180 degrees. This property can be proven using basic geometry.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Proof\"><\/span>Proof<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The triangle sum property, also known as the angle sum property of a triangle, states that the sum of the interior angles of a triangle is equal to 180 degrees. This property can be proved using Euclidean geometry as follows:<\/p>\n<p>Consider an arbitrary triangle ABC with three vertices A, B, and C. Draw a line segment CD parallel to side AB, where C is a point on side BC and D is a point on side AC. This divides the triangle ABC into two smaller triangles, ACD and CBD.<\/p>\n<p>Now, we know that the sum of the interior angles of a line is 180 degrees. Therefore, the sum of the angles ADC and BCD is 180 degrees.<\/p>\n<p>Next, we know that CD is parallel to AB, which means that the alternate interior angles are congruent. Therefore, angle ACD is congruent to angle B.<\/p>\n<p>Similarly, angle BCD is congruent to angle A.<\/p>\n<p>Therefore, we can conclude that the sum of the angles of triangle ABC is:<\/p>\n<p>angle A + angle B + angle C = angle A + angle ACD + angle BCD<\/p>\n<p>= angle A + angle B + 180 degrees &#8211; (angle A + angle B)<\/p>\n<p>= angle C + 180 degrees &#8211; angle C<\/p>\n<p>= 180 degrees<\/p>\n<p>Thus, we have proved that the sum of the angles of any triangle is equal to 180 degrees, which is the triangle sum property.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Some_other_Important_Angle_Properties_of_a_Triangle\"><\/span>Some other Important Angle Properties of a Triangle<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>The Interior Angle Sum of a Triangle is 180 degrees.<\/li>\n<li>The exterior angle of a triangle is the sum of the two opposite interior angles.<\/li>\n<li>The angle between two lines is equal to the angle between the lines&#8217; projections onto a third line.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Triangle Sum Property The Triangle Sum Property states that the sum of the measures of the angles of a triangle [&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":"Introduction to Angle Sum Triangle \u2013 Property, Proof and Solved Examples","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about intro angle sum triangle topic of maths in details explained by subject experts on infinitylearn.com. 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