Chapter 3, Problem 12CR

To determine

To Prove: The congruency of $\overline{SX}$ with respect to $\overline{SV}$

Explanation of Solution

Given information: $\angle T\cong \angle W$ , $\angle TSW\cong \angle XSW$ and $\overline{ST}\cong \overline{SW}$ is provided in the question which will help to find the solution.

Proof: Here, $\angle TSW\cong \angle XSW$ (given)

So that, SW bisects $\angle S$

And, $\overline{ST}\cong \overline{SW}$ (given)

So, $\angle SVT=\angle SXW$ (angle opposite to equal sides are equal)

Here, $\angle T\cong \angle W$ (given)

And, $\overline{SV}=\overline{SX}$ (sides opposite to equal angles are equal)

Hence, we can say that

  $\overline{SX}=\overline{SV}$