Chapter 4.5, Problem 7PPS

To determine

To prove:

  $\Delta XWZ\cong \Delta XYZ$ for the following figure:

  

Explanation of Solution

Given information:

  $\begin{array}{l}\angle W\cong \angle Y\\ \overline{WZ}\cong \overline{YZ}\end{array}$

  $\overline{XZ}$ bisects $\angle WZY$

Proof:

From the given figure:

  

According to the definition of angle bisector $\angle WZX\cong \angle YZX$ . Use the angle side angle (ASA) congruence postulate gets that: $\Delta XWZ\cong \Delta XYZ$

Hence proved.