Answer
It can follow that $\triangle RTS\cong\triangle RUV$ according to method SAS. (But first, prove $\overline{RS}\cong\overline{RV}$)
Work Step by Step
*STRATEGY:
1) Prove that $\overline{RS}\cong\overline{RV}$
2) Use method SAS to prove triangles congruent.
1) Prove that $\overline{RS}\cong\overline{RV}$
- Draw a line that goes through $R$ and passes $\overline{SV}$ at $H$ so that $\overline{RH}\bot\overline{SV}$.
Now we would try to prove that $\triangle RHS\cong\triangle RHV$
Since $\overline{RH}\bot\overline{SV}$, it follows that $\angle RHS=\angle RHV=90^{\circ}$
So, $\angle RHS\cong\angle RHV$
Furthermore,
- $\angle S\cong\angle V$ (given)
- $\overline{RH}\cong\overline{RH}$ (by Identity)
Therefore, according to method AAS, $\triangle RHS\cong\triangle RHV$
So $\overline{RS}\cong\overline{RV}$
2) We have $\overline{RS}\cong\overline{RV}$.
It is also given that
- $\angle S\cong\angle V$
- $\overline{ST}\cong\overline{VU}$
So, according to method SAS, $\triangle RTS\cong\triangle RUV$
