Question

Prove that AO=OC (Hint: the answer has nothing to do with rotation).

Answer 1

We have to prove diagonals of parallelogram ABCD bisects each other.
i.e, OA=OC & OB=OD
Now In ΔAOD and ΔBOC
AD=BC [opposite sides are equal]
∠ADO=∠CBO [alternate interior angle]
Similarly ∠DAO=∠BCO
∴ΔAOD≅ΔBOC by (ASA rule)
So, OA=OC & OB=OB