Prove that the diagonals of a parallelogram bisect each other.

Let us consider that AC and BD be the diagonals of the parallelogram ABCD.

To Prove: AC and BD bisect each other ie. OA=OC & OB=OD

Proof:

In ΔAOD and ΔBOC

AD=BC   [opposite sides are equal]

∠ADO=∠CBO  [alternate interior angle]

∠DAO=∠BCO [alternate interior angle]

∴ΔAOD≅ΔBOC  (by ASA rule)

So, OA=OC & OB=OB [ By CPCT]

Hence, the diagonals of a parallelogram bisect each other.