Lesson 7-2 Similar Polygons

Similar Polygons-polygons with the same shape, but not necessarily the same size. similar sign (∼)

Example: Write a similar statement for the polygons ABCD ∼ EFGH Be careful how you write them. They have to be the similar parts.

Scale Factor:  The ratio of the lengths of the corresponding sides of two similar polygons. Similarity Ratio:  Another name for scale factor. Example: a) 𝑥 10 = 9 6    So using cross products, we can say that 6x = 90, so x = 15 15 10 = 12 3𝑦−1 So, 120 = 15(3y – 1)   using cross products, or 120 = 45y – 15, so 135 = 45y Therefore y = 135 45 =3

Since the lengths of the sides of similar figures can be multiplied by the scale factor, so can the perimeters of the similar figures.

Example: 8 𝑥 = 4 3 Since AB∼QR and CD∼RS, we can write a proportion. 8 𝑥 = 4 3 4x = 24 X = 6 So QR = 6 So the sides of ABCDE are 8, 8, 4, 6, and 4, which has a perimeter of 30 units. Since we know the scale factor is 4 3 , we can say that the perimeter of RQPTS is 22.5 units.