Question

Points P and Q have been taken on opposite sides AB and CD respectively of a parallelogram ABCD such that AP=CQ. Show that AC and PQ bisect each other.

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Answer 1

by proving triangle OQC AND APO CONGURENT

Answer 2

Answer is in the attachment.

$\boxed{explanation}$

◆ Here , It is given that ABCD is a parallelogram, where P and Q are two points on AB and CD and AP = CQ

◆ We need to prove that AC and PQ bisect each other.

◆ We have taken two triangles AOP and COQ and we proved that they are congruent by (AAS criterion)

◆ As, the triangles are congruent we find

AO = CO and OP = OQ by (CPCT).

◆ As, AO = CO and OP = OQ we can say that AC and PQ bisect each other .