Chapter 4.4, Problem 14PSB

To determine

To Verify: $\angle WPZ$ is right angle.

Explanation of Solution

Given information: $WX=WZ,XY=YZ.$

Formula used: congruency of triangles, linear pair axiom

Proof:

  $\begin{array}{l}WX=WZ,XY=YZ.(\text{given})\\ WY=WZ(\text{Reflective}\text{property)}\\ \therefore \Delta WXY\cong \Delta WZY(\text{SSS})\\ \therefore \angle ZWP=\angle XWP(CPCT)\\ WP=WP(\text{Reflective}\text{property)}\\ \therefore \Delta WZP\cong \Delta WXP(\text{SAS})\\ \therefore \angle WPZ=\angle WPX(\text{CPCT})\\ \therefore \angle WPZ+\angle WPX={180}^{\circ }(\text{linear pair axiom})\\ \therefore \angle WPZ={90}^{\circ }=\angle WPX.\end{array}$