2. Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional. AB C DE F Similar Polygons

3. Naming Similar Polygons When naming similar polygons, the vertices (angles, sides) must be named in the corresponding order. AB CD PQ R S

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

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

6. Example: The two polygons are similar. Solve for x, y and z. 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. Step1: Write the proportion of the sides. Step 2: Replace the proportion with values. Step 4: Write separate proportions for each missing side and solve. 5 z x 10 y 15 30 20 B C A D F G E H

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

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