Similar Polygons Two polygons are similar if and

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