Question

Determine whether each pair of triangles is similar. If similarity exists, write a congruency statement relating to the two triangles. Give a justification for your answer.

Answer 1

We are going to use SAS. We need to find values of CR.

ΔCRK is right triangle, so from Pythagorean theorem

|CR|² +|RK|²=|CK|²

|CR|² + 4²= 5²

|CR| = 3

Corresponding sides should be in proportion:

OY/CR=YU/RK

16/4= 12/3

4/1 =4/1

These corresponding sides are in proportion, also we have m∠U=m∠R=90⁰.

So, we have 2 corresponding sides are in proportion and angles between them are congruent, so by SAS these triangles are similar. Because of it their corresponding angles are congruent:

m∠O=m∠C, m∠Y=m∠R, m∠U=m∠K.