EXAMPLE 1 Use similarity statements In the diagram, ∆RST ~ ∆XYZ a. List all pairs of congruent angles. b. Check that the ratios of corresponding side lengths are equal. c. Write the ratios of the corresponding side lengths in a statement of proportionality.

EXAMPLE 1 Use similarity statements SOLUTION a. R = ~ X, S Y T Z and RS XY = 20 12 5 3 b. ; ST = 30 18 5 3 YZ ; TR ZX = 25 15 5 3 c. Because the ratios in part (b) are equal, YZ RS XY = ST TR ZX .

GUIDED PRACTICE for Example 1 1. Given ∆ JKL ~ ∆ PQR, list all pairs of congruent angles. Write the ratios of the corresponding side lengths in a statement of proportionality. J = ~ P, K Q L R and JK PQ KL QR LJ RP ; ANSWER