Question

p and q are the points of trisection of the diognals bd of a parallelogram ABCD. prove that cq is parallel to ap​

Answer 1

Answer:

We know that, diagonals of a parallelogram bisect each other.

⇒ OA=OC and OB=OD

Since P and Q are point of trisection of BD

∴ BP=PQ=QD

Now, OB=OD and BP=QD

⇒ OB−BP=OD−QD

⇒ OP=OQ

In quadrilateral APCQ, we have

OA=OC and OP=OQ

Diagonals of quadrilateral APCQ bisect each

∴ APCQ is a parallelogram.

⇒ AP∥CQ [ Opposite sides are parallel in parallelogram ]