Chapter 6.3, Problem 16PPS

To determine

The proof that ZMY is an isosceles triangle.

Explanation of Solution

Given:

WXYZ is a parallelogram.

  $\angle W\cong \angle X\text{ and M is the midpoint of }\overline{\text{WX}}\text{.}$

Calculation:

As WXYZ is a parallelogram,

  $\overline{WZ}\cong \overline{XY}.$

As, M is the midpoint of line segment $\overline{\text{WX}}$ , according to the midpoint theorem,

  $\overline{WM}\cong \overline{MX}.$

Also, $\angle W\cong \angle X$ .

Therefore, according to SAS congruence,

  $\Delta ZWM\cong \Delta YXM$ .

Also, according to CPCTC, $\overline{ZM}\cong \overline{YM}.$

Hence, ZMY is an isosceles triangle.