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 5.7 Properties of Similar triangles Perimeters of similar triangles: Perimeters of similar triangles are in the same ratio as their corresponding sides and this ratio is called the scale factor. In figure 5.6 there are two similar triangles . D LMN and D PQR.  Figure 5.6 This ratio is called the scale factor. Perimeter of D LMN = 8 + 7 + 10 = 25 Perimeter of D PQR = 6 + 5.25 + 7.5 = 18.75 Thus, the perimeters of two similar triangles are in the ratio of their scale factor. Areas of similar triangles: The ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides, i.e. the square of the scale factor.  Figure 5.7 D ABC ~ D PQR To prove that Draw perpendicular from A and P to meet seg.BC and seg.QR at D and S respectively. Since D ABC ~ D PQR also Ð B @ Ð Q In D ABD and D PQS also Ð B @ Ð Q and Ð ADB @ Ð PSQ \ D ABD ~ D PQS by A A test.   Thus the areas of two similar triangles are in the same ratio as the square of their scale factors. Index 5.1 Introduction 5.2 Ratio And Proportionality 5.3 Similar Polygons 5.4 Basic Proportionality Theorem 5.5 Angle Bisector Theorem 5.6 Similar Triangles 5.7 Properties Of Similar Triangles
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