Chapter 5.5, Problem 8PSA

To determine

To prove:The diagonals of a parallelogram bisect each other.

Explanation of Solution

Given Information:

  $ABCD$ is a parallelogram

Formula used:

Corresponding parts of two congruent triangles are congruent.

Calculation:

  

Let $ABCD$ be a parallelogram with diagonals $AC$ and $BD$ intersecting at $O$

In $\Delta AOD\text{and}\Delta COB,$

  $\angle DAO=\angle BCO$ … (Alternate interior angles)

  $AD=BC$ … (Opposite sides of a parallelogram are equal)

  $\angle ADO=\angle CBO$ … (Alternate interior angles)

  $\Delta AOD\cong \Delta COB$ … (ASA congruency rule)

As we know that the corresponding parts of two congruent triangles are congruent, then we have

  $AO=CO\text{and}OD=OB$

Hence, the diagonals of a parallelogram bisect each other.