# Chapter 3 - Section 3.2 - Corresponding Parts of Congruent Triangles - Exercises - Page 152: 33

- 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)

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