Chapter 4.4, Problem 2PSA

To determine

To Prove: $WX=WY.$

Explanation of Solution

Given information: WZ is perpendicular bisector of XY.

Formula used: congruency of triangles.

Proof: WZ is perpendicular bisector of XY (given)

  $\begin{array}{l}\therefore \angle WZX=\angle WZY(\text{Each}\text{equal}{90}^{\circ })\\ \text{and}ZX=ZY\\ WZ=WZ(\text{Reflection}\text{property)}\\ \therefore \Delta WZX\cong \Delta WZY(\text{SAS})\\ \therefore WX=WY(CPCT)\\ \therefore \Delta WXY\text{is}\text{isosceles}\text{.}\end{array}$