EQ: How do you identify similar polygons? 7.2 OBJ: Identify similar polygons EQ: How do you identify similar polygons?

VOCABULARY Two polygons are similar polygons if corresponding angles are congruent and corresponding side lengths are proportional.

VOCABULARY Two polygons are similar polygons if corresponding angles are congruent and corresponding side lengths are proportional. Ratio = scale factor.

List all pairs of congruent angles. a. Example 1 Use Similarity Statements PRQ ~ STU. List all pairs of congruent angles. a. Write the ratios of the corresponding sides in a statement of proportionality. b. Check that the ratios of corresponding sides are equal. c. SOLUTION PR ST 10 8 5 4 = , RQ TU 20 16 , and QP US 15 12 . The ratios of corresponding sides are all equal to 5 4 . 4

Example 1 Use Similarity Statements PRQ ~ STU. The ratios of corresponding sides are all equal to 5 4 . 5

Example 2 Determine Whether Polygons are Similar Determine whether the triangles are similar. If they are similar, write a similarity statement and find the scale factor of Figure B to Figure A. SOLUTION GH MK 9 12 9 ÷ 3 12 ÷ 3 = 3 4 HJ KL 16 12 ÷ 4 16 ÷ 4 JG LM 15 20 15 ÷ 5 20 ÷ 5 G  M, H  K, and J  L. Therefore, the corresponding angles are congruent. GHJ ~ MKL. 6

Checkpoint Determine Whether Polygons are Similar Determine whether the polygons are similar. If they are similar, write a similarity statement and find the scale factor of Figure B to Figure A. 1.

Checkpoint Determine Whether Polygons are Similar Determine whether the polygons are similar. If they are similar, write a similarity statement and find the scale factor of Figure B to Figure A. 1.

Theorem 7.1 Perimeters of Similar Polygons If two polygons are similar, then the ratio of their perimeters is equal to the ratio of their corresponding side lengths.