Question

# Points P and Q have been taken on opposite sides AB and CD respectively of a parallelogram ABCD such that AP = CQ. Which of the following is correct?AC = CDAC and PQ bisect each other.AC = PQNone of the above

Solution

## The correct option is B AC and PQ bisect each other.In triangles AOP  and COQ, AP=CQ (Given) ∠1=∠2 (Alternate interior angles) ∠3=∠4 (Vertically opposite angles)∴AOP≅COQ (By AAS congruence criterion)  ∴OA=OC and OP=OQ (CPCT) Hence, AC and PQ bisect each other.

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