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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?

A
AC and PQ bisect each other.
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B
AC = PQ
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C
AC = CD
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D
None of the above
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Solution

The correct option is A 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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