Chapter 3, Problem 14RP

To determine

To Prove: The congruency of $\overline{WY}$ with respect to $\overline{YA}$

Explanation of Solution

Given information: $\overline{VX}\cong \overline{VZ}$ , Y is the mid-point of $\overline{XZ}$ is provided in the question which will help to find the solution.

Proof: Here, In $\Delta WXY$ and $\Delta AYZ$

  $\overline{VX}\cong \overline{VZ}$(given)

And, $\angle VXZ=\angle VZX$ (angle opposite to equal sides are equal)

And, XY = YZ ( $\because$ Y is the mid-point of $\overline{XZ}$ )

And, WX = AZ ( $\because$

  $\overline{VX}\cong \overline{VZ}$ )

Hence, $\Delta WXY\cong \Delta AYZ$ (by side angle side rule)

So, $\overline{WY}\cong \overline{YA}$ (corresponding parts of congruent triangles)