Lesson 5 -2 Similar Polygons Lesson 5 -2: Similar Polygons 1

Similar Polygons Definition: Two polygons are similar if: 1. Corresponding angles are congruent. 2. Corresponding sides are in proportion. Two polygons are similar if they have the same shape not necessarily have the same size. Scale Factor: The scale factor is the ratio between a pair of corresponding sides. Lesson 5 -2: Similar Polygons 2

Naming Similar Polygons When naming similar polygons, the vertices (angles, sides) must be named in the corresponding order. A D P B C Lesson 5 -2: Similar Polygons Q S R 3

Example- A 15 The two polygons are similar. 20 Solve for x, y and z. B E D y 30 x H 10 C 5 F z G Step 1: Write the proportion of the sides. Step 2: Replace the proportion with values. Step 3: Find the scale factor between the two polygons. Note: The scale factor has the larger quadrilateral in the numerator and the smaller quadrilateral in the denominator. Step 4: Write separate proportions for each missing side and solve. Lesson 5 -2: Similar Polygons 4

If ABC ~ ZYX, find the scale factor from Example: ABC to ZYX. Scale factor is same as the ratio of the sides. Always put the first polygon mentioned in the numerator. C 10 B 5 Y X 14 The scale factor from ABC to ZYX is 2/1. 18 7 9 Z A What is the scale factor from ZYX to ABC? Lesson 5 -2: Similar Polygons ½ 5