SIMILAR POLYGONS Identify similar figures Solve problems involving

SIMILAR POLYGONS • Identify similar figures • Solve problems involving scale factors Ford Model A (? )

IDENTIFY SIMILAR FIGURES When two polygons have the same shape but may be different in size, they are called similar polygons,

Key Concept Similar Polygons Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional D H 10 5 8 4 E A 5 B 6 C 2. 5 F 3 G

The order of the vertices in a similarity statement is important. It identifies the corresponding angles and the corresponding sides. D H 10 5 8 4 E A 5 B 6 C 2. 5 ABCD ~ EFGH F 3 G

Example 1 – Similar Polygons Determine whether the figures are similar. Justify your answer. F B 12 A 6 4. 5 E 30° C 6√ 3 • All right angles are congruent, so • Since • By the third angle theorem, 4. 5√ 3 30° 9 D

Example 1 – Similar Polygons continued Determine whether the figures are similar. Justify your answer. F B 12 A 6 4. 5 E 30° C 4. 5√ 3 30° 9 D 6√ 3 Now, let’s determine if corresponding sides are proportional.

SCALE FACTORS When you compare the lengths of corresponding sides of similar figures, you usually get a numerical ratio. This ratio is called the scale factor.

Example 2 – Scale Factor Some special effects in movies are created using miniature models. In a recent movie, a model sportsutility vehicle (SUV) 22 inches long was created to look like the real 14⅔-foot (176 inch) SUV. What is the scale factor of the model compared to the real SUV? Volvo XC 90

Example 3 – Proportional Parts and Scale Factor A R B S x V To find x: 18 T 3 E 4 C U (y + 2) 5 D

Example 3 – Proportional Parts and Scale Factor cont. A R B S x To find y: V 18 T 3 E 4 C U (y + 2) 5 D

Example 4 – Scale Factors on Maps