{"id":5832,"date":"2013-05-06T12:30:00","date_gmt":"2013-05-06T12:30:00","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=5832"},"modified":"2014-12-02T08:27:02","modified_gmt":"2014-12-02T08:27:02","slug":"similar-triangles","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2013\/05\/06\/similar-triangles\/","title":{"rendered":"Similar Triangles"},"content":{"rendered":"

Overview:\u00a0 What Are Similar Triangles?<\/strong>
\nTwo triangles are similar if they each have two angles that have the same measurement, and the lengths of the corresponding sides are proportionate.\u00a0 Therefore, one triangle can be made to measure the same as the other one by multiplying each side by the same factor.\u00a0 For example, given two triangles \u2206ABC and \u2206DEF, angles A and D measure the same, angles B and E measure the same, and angles C and F measure the same.\u00a0 The angles that measure the same are shown with the same symbol on each triangle.<\/p>\n

https:\/\/schooltutoring.com\/wp-content\/uploads\/sites\/8\/2013\/04\/similar_triangles.gif<\/a>
\nWhat Are Proportionate Sides?<\/strong><\/p>\n

If the lengths of corresponding sides are in the same ratio to each other, then they are proportionate.\u00a0 For example, in the above similar triangles, the length of DF is 4, the length of DE is 5, and the length of EF is 6.\u00a0 The length of AC is 8, the length of AB is 10, and the length of BC is 12.\u00a0 The ratio of DF\/AC is 4\/8, simplified as 1\/2, the ratio of DE\/AB is 5\/10, simplified to 1\/2, and the ratio of EF\/BC is 6\/12, simplified to 1\/2.<\/p>\n

Using Algebra to Find Unknown Measures<\/strong><\/p>\n

Suppose all that was known were that two triangles were similar, the measurements of three sides of one triangle, and the measurements of two sides of the other similar triangle.\u00a0 In this example, the measurement of DE is 3, DF is 5, and EF is 7. The measurement of AB is 6 and BC is 10.\u00a0 What is the measurement of AC?\u00a0 In this example, AB\/DE =AC\/EF.\u00a0 Substituting the measurements of sides, 6\/3 =x\/7, where x represents the measurement of AC.\u00a0 So 3x = 7(6), or 3x = 42.\u00a0 Dividing both sides by 3, x =14.\u00a0 The measurement of AC is 14.<\/p>\n

Are Special Triangles Similar?<\/strong>
\nThe isosceles right triangle, with measurements of 900<\/sup>, 450<\/sup>, and 450<\/sup>, is one type of special triangle. The lengths of its sides are determined by the Pythagorean theorem.\u00a0 Both sides that make up the right angle have the same length, a ,and the hypotenuse equals a\u221a2.\u00a0 Similarly, a right triangle with measurements 300<\/sup>, 600<\/sup>, and 900<\/sup>, will have a shorter leg of b, a longer leg of b\u221a3, and a hypotenuse of 2b.\u00a0 Any isosceles right triangle will be similar to any other isosceles right triangle, because they have angle measures in common and side lengths in proportion, and any 300<\/sup>-600<\/sup>-900<\/sup> right triangle will be similar to any other, but the two types of right triangles are not similar because they only have one angle, the right angle, in common.<\/p>\n

Can Other Polygons Be Similar?<\/strong>
\nIn order for polygons to be similar to each other, both the proportionality requirement and the \u00a0equal angle requirement must be met.\u00a0 For example, the definition of a square is that all four sides are equal and that all angles are right angles.\u00a0 All squares are similar to one another, because their angles have a common measure, and their sides are in proportion.<\/p>\n

Interested in geometry tutoring<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n

SchoolTutoring Academy<\/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 Cambridge, MA visit: Tutoring in Cambridge, MA<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview:\u00a0 What Are Similar Triangles? Two triangles are similar if they each have two angles that have the same measurement, and the lengths of the corresponding sides are proportionate.\u00a0 Therefore, one triangle can be made to measure the same as the other one by multiplying each side by the same factor.\u00a0 For example, given two […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[10,13],"tags":[1633,1703],"class_list":["post-5832","post","type-post","status-publish","format-standard","hentry","category-geometry","category-pre-algebra","tag-similar-triangles","tag-special-triangles-proportion"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/5832","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\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=5832"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/5832\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=5832"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=5832"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=5832"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}