Points P and Q have been taken on opposite sides AB and CD, respectively of a parallelogram ABCD such that AP = CQ (Fig. 8.6). Show that AC and PQ bisect each other.

Question

Philoid · Accepted Answer

Joining AQ and PC.

Since ABCD is a parallelogram, AB||DC and AP||QC.

Given, AP = CQ.

APCQ is a parallelogram.

We know, diagonals of a parallelogram bisect each other.

Hence AC and PQ bisect each other.