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
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.