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  P   S,  R   T, and  Q   U. a. PR ST RQ TU QP US = = b. c. PR ST = =, RQ TU = =, and QP US = =. The ratios of corresponding sides are all equal to 5 4.

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 Check whether the corresponding angles are congruent. 1. From the diagram, you can see that  G   M,  H   K, and  J   L. Therefore, the corresponding angles are congruent.

Example 2 Determine Whether Polygons are Similar GH MK ÷ 3 12 ÷ 3 = = 3 4 = HJ KL ÷ 4 16 ÷ 4 = = 3 4 = JG LM ÷ 5 20 ÷ 5 = = 3 4 = All three ratios are equal, so the corresponding side lengths are proportional. ANSWER By definition, the triangles are similar.  GHJ ~  MKL. The scale factor of Figure B to Figure A is 3 4. Check whether the corresponding side lengths are proportional. 2.

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 ANSWER yes;  XYZ ~  DEF ; 2 3 ANSWER no ≠