Answer
Proof for the problem:
1. $\angle 3\cong\angle 4$ (1. Given)
2. $\angle 1\cong\angle 2$ (2. Given)
3. $\overline{ST}\cong\overline{ST}$ (3. Identity)
4. $\triangle RST\cong\triangle VST$ (4. ASA)
Work Step by Step
1) First, it is given that $\angle 3\cong\angle 4$
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 the included side of $\triangle RST$ are congruent with 2 corresponding angles and the included side of $\triangle VST$.
So we would use ASA to prove triangles congruent.
Now we would construct a proof for the problem:
1. $\angle 3\cong\angle 4$ (1. Given)
2. $\angle 1\cong\angle 2$ (2. Given)
3. $\overline{ST}\cong\overline{ST}$ (3. Identity)
4. $\triangle RST\cong\triangle VST$ (4. ASA)
