Chapter 4, Problem 14RP

To determine

To Verify: $WR=RZ$

Explanation of Solution

Given information: $\angle WXY=\angle ZYX,WX=ZY.$

Formula Used: Congruency of triangle and properties of angles.

Proof:

  $\angle WXY=\angle ZYX$ And $WX=ZY$ (given)

  $\begin{array}{l}XY=XY(common)\\ \therefore \Delta WXY\cong \Delta ZYX(SAS)\\ \angle XWY=\angle YZX.\end{array}$

Also, $\angle WRX=\angle ZRY$ (vertically opposite angles)

  $\begin{array}{l}\therefore \Delta WRY\cong \Delta ZRY(AAS)\\ \therefore WR=RZ(CPCT)\end{array}$