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.
• B. AC = PQ
• C. AC = CD
• D. None of the above

Answer 1

The correct option is A AC and PQ bisect each other.

In triangles AOP and COQ,
$AP=CQ\left(\text{Given}\right)$
$\angle 1=\angle 2\left(\text{Alternate interior angles}\right)$
$\angle 3=\angle 4\left(\text{Vertically opposite angles}\right)\therefore AOP\cong COQ\text{(By AAS congruence criterion)}$

$\therefore OA=OC\text{and}OP=OQ\text{(CPCT)}$
$\text{Hence, AC and PQ bisect each other.}$