Consider the below parallelogram ABCD with diagonals AC and BD.

**Given:**We know that opposite sides of parallelogram are equal.

AB = CD

AD = BC

Also in parallelogram, opposite sides are parallel to each other.

AB || CD

AD || BC

**To prove:**Diagonals bisect each other.

AO = OC

DO = OB

**Proof**:

Consider triangle AOD and BOC.

AD = BC (given)

∠DAO = ∠BCO (alternate interior angle)

∠ADO = ∠OBC (alternate interior angle)

By ASA congruency condition, both the triangles are congruent.

\mathtt{\triangle AOD\cong \triangle BOC}

By rule of congruency, we can say that AO = OC and DO = OB.

Hence in parallelogram, the diagonals bisect each other.