Question

In the following diagram, AP and BQ are equal and parallel to each other.
Prove that: AB and PQ bisect each other.

Answer 1

In the figure, AP and BQ are equal and parallel to each other. 
∴ AP = BQ and AP || BQ. 
We need to prove that AB and PQ bisect each other.

The corresponding parts of the congruent triangles are congruent.
∴ OP = OQ                ...[ c. p. c .t ]
OA = OB                    ...[ c. p. c .t ]
Hence AB and PQ bisect each other.