Question

P and Q are points of trisection of the diagonal BD of a parallelogram ABCD.
Prove that CQ || AP and AC bisects PQ.

Answer 1

Step-by-step explanation:

OA=OC and OB=OD.

Since P and Q are points of trisection of BD.

∴BP=PQ=QD.

Now, OB=OD and BP=QD

⇒OP−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...