## Elementary Geometry for College Students (5th Edition)

It can follow that $\triangle RTS\cong\triangle RUV$ according to method SAS. (But first, prove $\overline{RS}\cong\overline{RV}$)
*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, $\triangle RTS\cong\triangle RUV$