Chapter 13.9, Problem 2WE

To determine

To prove: diagonals of a parallelogram bisect each other.

Explanation of Solution

Given information:

  $ABCD$ is a parallelogram with two diagonals bisecting at a point $O$ .

  

Calculation:

We have to show $\overline{DO}=\overline{OB}$ and $\overline{AO}=\overline{OC}$ .

From $\Delta AOC$ and $\Delta DOC$ ,

  $\begin{array}{l}\angle AOB=\angle DOC\\ \angle BDA=\angle ODC\\ \angle DCO=\angle OAB\end{array}$

Therefore, since $\overline{DC}=\overline{AB}$ ,

  $\Delta AOB=\Delta DOC\Rightarrow \overline{DO}=\overline{OB}\text{ and }\overline{AO}=\overline{OC}$

Hence proved that diagonals are bisecting each other.