Question

P and Q are the points of trisection of the diagonal BD of a parallelogram AB Prove that CQ is parallel to AP. Prove also that AC bisects PQ.

Answer 1

We know that, diagonals of a parallelogram bisect each other

∴OA = OC and OB = OD

Since P and Q are point of intersection of BD

∴BP = PQ = QD

Now, OB = OD and BP = QD

 ⇒ OB - BP = OD - QD

⇒ OP = OQ

Thus in quadrilateral APCQ, we have

OA = OC and OP = OQ

⇒ diagonals of quadrilateral APCQ bisect each other

∴APCQ is a parallelogram

Hence AP || CQ