Chapter 9, Problem 3CUR

To determine

To prove: that $\overline{MN}$ bisects $\overline{WY}$ .

Explanation of Solution

Given information:$\overline{MN}$ is the median of a trapezoid $WXYZ$ .

Calculation:

Consider that $\overline{MN}$ is the median of trapezoid $WXYZ$ .

For proving that $\overline{MN}$ bisects $WY$ , first prove congruent $\Delta VMW$ to $\Delta VNY$

Consider the triangles $\Delta VMW$ and $\Delta VNY$

  $\begin{array}{c}\angle MVW=\angle YVN\\ \angle VWM=\angle VYN\\ MW=YN\end{array}$

Hence, the triangles are congruent $\Delta VMW\cong \Delta VNY$ .

Since both triangles are equal so corresponding sides will also be equal:

  $WV=YV$

Hence,

$\overline{MN}$ bisects $WY$ .