Elementary Geometry for College Students (5th Edition)

Given $\triangle RST\cong\triangle RVU$, it follows that $\triangle RSU\cong\triangle RVT$, according to method SAS.
Given $\triangle RST\cong\triangle RVU$, we can deduce that 1) $\overline{RS}\cong\overline{RV}$ 2) $\angle S\cong\angle V$ 3) $\overline{ST}\cong\overline{VU}$ Since $\overline{ST}\cong\overline{VU}$, it follows that $$\overline{ST}+\overline{TU}\cong\overline{VU}+\overline{TU}$$$$\overline{SU}\cong\overline{TV}$$ Considering $\triangle RSU$ and $\triangle RVT$, we have 1) $\overline{SU}\cong\overline{TV}$ 2) $\angle S\cong\angle V$ 3) $\overline{RS}\cong\overline{RV}$ Therefore, according to method SAS, $\triangle RSU\cong\triangle RVT$