Chapter 5.2, Problem 31PPS

To determine

To proof: The line segment $\overline{WY}$ is the median.

Answer to Problem 31PPS

The proof that the line segment $\overline{WY}$ is the median is stated below.

Explanation of Solution

  $\Delta XYZ$ is isosceles. So, $XY=ZY$

Now,

  $\overline{WY}$ bisects $\angle Y$ .

  $\angle XYW=\angle ZYW$

By the reflexive congruence property.

  $WY=WY$

BY SAS congruence property.

  $\Delta XWY\cong \Delta ZWY$

By CPCT.

  $\overline{XW}=\overline{ZW}$

Thus, $\overline{WY}$ is the median.

Hence proved.