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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?
  1. AC = CD
  2. AC and PQ bisect each other.
  3. AC = PQ
  4. None 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)AOPCOQ (By AAS congruence criterion) 

OA=OC and OP=OQ (CPCT)
Hence, AC and PQ bisect each other.

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