Answer
Proof for the problem:
1. $\angle R$ and $\angle V$ are right $\angle$s (1. Given)
2. $\triangle RST$ and $\triangle VST$ are right triangles. (2. A triangle that has one right angle is a right triangle)
3. $\overline{ST}\cong\overline{ST}$ (3. Identity)
4. $\overline{RT}\cong\overline{VT}$ (4. Given)
5. $\triangle RST\cong\triangle VST$ (5. HL)
Work Step by Step
1) First, it is given that $\angle R$ and $\angle V$ are right $\angle$s.
So, $\triangle RST$ and $\triangle VST$ are right triangles.
2) It is also given that $\overline{RT}\cong\overline{VT}$
3) By identity, we find that $\overline{ST}\cong\overline{ST}$
Now we see that the leg and hypotenuse of right $\triangle RST$ are congruent with the leg and hypotenuse of right $\triangle VST$.
So we would use HL 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. $\triangle RST$ and $\triangle VST$ are right triangles. (2. A triangle that has one right angle is a right triangle)
3. $\overline{ST}\cong\overline{ST}$ (3. Identity)
4. $\overline{RT}\cong\overline{VT}$ (4. Given)
5. $\triangle RST\cong\triangle VST$ (5. HL)
