There are three main methods to prove triangles are similar. The information provided in the question dictates which approach to attempt. Below are the details on each. <\/span><\/p>\n Use this method when the lengths of all three sides of both triangles are known . The goal is to show that the ratio between each pair of corresponding sides is equal. This is accomplished by creating and evaluating fractions out of the pairs of corresponding sides. When performing these calculations, there are two important things to note:<\/span><\/p>\n If all of the ratios are the same, this means the sides are proportional, which \u00a0is the definition of a similar triangle.<\/span><\/p>\n <\/p>\n Ex:<\/b> The following triangles are similar since <\/span><\/p>\n 3 \/ 9 = <\/span>1 \/ 3<\/b><\/p>\n 4 \/ 12 = <\/span>1 \/ 3<\/b><\/p>\n 5 \/ 15 = <\/span>1 \/ 3<\/b> \u00a0<\/span><\/p>\n Use this method when given:<\/span><\/p>\n The goal is to show that two of the angles are the same in each triangle. Because the sum of the interior angles of a triangle is always 180 degrees, knowing two of the angles are the same means we know the third angle must be the same as well. Note that some schools require this reasoning to be included with the proof as well. This means that if two of the angles in a triangle match two of the angles in the other triangle (equal corresponding angles), then the triangles are similar.<\/span><\/p>\n <\/p>\n Ex: <\/b>The following triangles are similar since it\u2019s given that two of the angles in each triangle are the same. <\/span><\/p>\n Use this method when presented with an \u00a0\u201cangle sandwich\u201d in each triangle. This term refers to the situation where an angle, as well as the two sides surrounding it, are defined. If the angles apart of the \u201cangle sandwich\u201d are the same, check if the ratios between the two pairs of corresponding sides are equal (as described in side-side-side similarity above). Once this is proven to be true, it\u2019s enough information to conclude that they\u2019re similar triangles. <\/span><\/p>\n Ex: <\/b>The following triangles are similar since the angles are equal and <\/span><\/p>\n 3 \/ 7 = <\/span>.43<\/b><\/p>\n 3 \/ 7 = <\/span>.43<\/b><\/p>\n If any of the above cases are false, then the triangles are not similar! Explaining why is an acceptable disproof. \u00a0\u00a0\u00a0<\/span><\/p>\n Interested in math tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n SchoolTutoring Academy<\/a>\u00a0<\/span>is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Escondido, CA<\/a>: visit: Tutoring in Escondido, CA.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":" Definition: Similar triangles have equal corresponding angles and proportional sides. \u00a0 There are three main methods to prove triangles are similar. The information provided in the question dictates which approach to attempt. Below are the details on each. Side-Side-Side Similarity: Use this method when the lengths of all three sides of both triangles are known […]<\/p>\n","protected":false},"author":17,"featured_media":66976,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[11,3016,18,1],"tags":[],"class_list":["post-66972","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-math-fundamentals","category-resources","category-trigonometry","category-uncategorized"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/66972","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/17"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=66972"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/66972\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media\/66976"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=66972"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=66972"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=66972"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Side-Side-Side Similarity:<\/b><\/h3>\n
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<\/a><\/p>\nAngle-Angle Similarity:<\/b><\/h3>\n
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<\/a><\/p>\nSide-Angle-Side Similarity: <\/b><\/h3>\n
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