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Two triangles are Similar if the only difference is size (and possibly the need to turn or flip one around). These triangles are all similar: (Equal angles have been marked with the same number of arcs) Some of them have different sizes and some of them have been turned or flipped. For similar triangles: All corresponding angles are equal and All corresponding sides have the same ratio Also notice that the corresponding sides face the corresponding angles. For example the sides that face the angles with two arcs are corresponding. Corresponding SidesIn similar triangles, corresponding sides are always in the same ratio. For example: Triangles R and S are similar. The equal angles are marked with the same numbers of arcs. What are the corresponding lengths?
Calculating the Lengths of Corresponding SidesWe can sometimes calculate lengths we don't know yet.
Step 1: Find the ratioWe know all the sides in Triangle R, and The 6.4 faces the angle marked with two arcs as does the side of length 8 in triangle R. So we can match 6.4 with 8, and so the ratio of sides in triangle S to triangle R is: 6.4 to 8 Now we know that the lengths of sides in triangle S are all 6.4/8 times the lengths of sides in triangle R. Step 2: Use the ratio
a faces the angle with one arc as does the side of length 7 in triangle R. a = (6.4/8) × 7 = 5.6 b faces the angle with three arcs as does the side of length 6 in triangle R. b = (6.4/8) × 6 = 4.8 Done!
Did You Know? Similar triangles can help you estimate distances. Copyright © 2017 MathsIsFun.com |