Answer
Proof for the problem:
1. $\angle R$ and $\angle V$ are right $\angle$s. (1. Given)
2. $\angle R\cong\angle V$ (2. Both of these corresponding angles are $90^o$)
3. $\angle 1\cong\angle 2$ (3. Given)
4. $\overline{ST}\cong\overline{ST}$ (4. Identity)
5. $\triangle RST\cong\triangle VST$ (5. AAS)
Work Step by Step
1) First, it is given that $\angle R$ and $\angle V$ are right $\angle$s.
Therefore, $\angle R\cong\angle V$
2) It is also given that $\angle 1\cong\angle 2$
3) By identity, we find that $\overline{ST}\cong\overline{ST}$
Now we see that 2 angles and a non-included side of $\triangle RST$ are congruent with 2 corresponding angles and a non-included side of $\triangle VST$.
So we would use AAS to prove triangles congruent.
Now we would construct a proof for the problem:
1. $\angle R$ and $\angle V$ are right $\angle$s. (1. Given)
2. $\angle R\cong\angle V$ (2. Both of these corresponding angles are $90^o$)
3. $\angle 1\cong\angle 2$ (3. Given)
4. $\overline{ST}\cong\overline{ST}$ (4. Identity)
5. $\triangle RST\cong\triangle VST$ (5. AAS)
