Question

the triangles in the pair are similar. △stu ~ △stu
a. identify the congruent corresponding angles.

move an angle into each space provided.

∠s≅
∠t≅
∠u≅
∠u ∠s ∠t
b. which ratios identify the proportional sides of each triangle? select all that apply.

Explanation:

Step1: Recall property of similar triangles

In similar triangles, corresponding angles are congruent. For $\triangle STU\sim\triangle S'T'U'$, $\angle S$ corresponds to $\angle S'$, $\angle T$ corresponds to $\angle T'$ and $\angle U$ corresponds to $\angle U'$.

Step2: Identify the proportional - side ratios

For similar triangles $\triangle STU\sim\triangle S'T'U'$, the ratios of corresponding sides are equal. The possible ratios of corresponding sides are $\frac{ST}{S'T'}$, $\frac{TU}{T'U'}$, $\frac{SU}{S'U'}$.

Answer:

a. $\angle S\cong\angle S'$, $\angle T\cong\angle T'$, $\angle U\cong\angle U'$
b. $\frac{ST}{S'T'}$, $\frac{TU}{T'U'}$, $\frac{SU}{S'U'}$ (assuming these are among the options not fully shown in the problem - but these are the general forms of ratios of corresponding sides of similar triangles)