Chapter 3, Problem 14CR

To determine

To Prove: The congruency of $\angle XWR$ with respect to $\angle RXW$

Explanation of Solution

Given information: $\Delta ZWX$ is isosceles with base $\overline{WX}$ , $\overrightarrow{WR}$ bisects $\angle XWZ$ and $\overrightarrow{XR}$ bisects $\angle ZXW$ is provided in the question which will help to find the solution.

Proof: Here, WX = ZX ( $\because$

  $\Delta ZWX$ is isosceles)

And, $\angle ZWX=\angle ZXW$ (angle opposite to equal sides are equal)

And, $\angle ZWR=\angle RWX,\angle RXW=\angle ZXR$ ( $\because$

  $\overrightarrow{WR}$ bisects $\angle XWZ$ and $\overrightarrow{XR}$ bisects $\angle ZXW$ )

And, $2\angle RWX=2\angle RXW$

Hence, $\angle XWR=\angle RXW$

Hence, we can say that

  →$\angle XWR\cong \angle RXW$