Answer
- Prove that $\triangle WRS\cong\triangle WRU$ by method SAS to deduce $\angle RSW\cong\angle RUW$
- From the deduction plus some other given information and identity, prove that $\triangle SRV\cong\triangle URT$ by method ASA.
Work Step by Step
- Prove that $\triangle WRS\cong\triangle WRU$ by method SAS to deduce $\angle RSW\cong\angle RUW$
- From the deduction plus some other given information and identity, prove that $\triangle SRV\cong\triangle URT$ by method ASA.
* Prove that $\triangle WRS\cong\triangle WRU$
1) $\vec{RW}$ bisects $\angle SRU$ (Given)
2) $\angle WRS\cong\angle WRU$ (the bisector of an angle divides it into 2 congruent angles)
3) $\overline{RS}\cong\overline{RU}$ (Given)
4) $\overline{RW}\cong\overline{RW}$ (Identity)
So now 2 lines and the included angle of $\triangle WRS$ are congruent with 2 corresponding lines and the included angle of $\triangle WRU$.
5) $\triangle WRS\cong\triangle WRU$ (SAS)
6) $\angle RSW\cong\angle RUW$ (CPCTC)
* Prove that $\triangle SRV\cong\triangle URT$
7) $\angle RSV\cong\angle RUT$ (proved in 5)
8) $\overline{RS}\cong\overline{RU}$ (Given)
9) $\angle SRV\cong\angle URT$ (Identity)
So now 2 angles and the included side of $\triangle SRV$ are congruent with 2 corresponding angles and the included side of $\triangle URT$.
10) $\triangle SRV\cong\triangle URT$ (ASA)
