# Similar Polygons Two polygons are similar if and

- Slides: 8

Similar Polygons Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional. F C A B D E

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

Scale Factor The scale factor is the ratio between a pair of corresponding sides. 24 8 10 30 or or

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

Example: A The two polygons are similar. Solve for x, y and z. 15 20 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.

If two triangles are similar, then the perimeters are proportional to the measures of the corresponding sides. A D B C E F

Example: Given: ΔABC ~ ΔDEF, AB = 15, AC = 20, BC = 25, and DF = 4. Find the perimeter of ΔDEF. The perimeter of ΔABC is 15 + 20 + 25 = 60. Side DF corresponds to side AC, so we can set up a proportion as: E B 15 A 25 20 D C 4 F