Question

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

Answer 1

Figure can be drawn as follows:

We have P and Q as the points of trisection of the diagonal BD of parallelogram ABCD.

We need to prove that AC bisects PQ. That is, .

Since diagonals of a parallelogram bisect each other.

Therefore, we get:

and

P and Q as the points of trisection of the diagonal BD.

Therefore,

and

Now, and

Thus,

AC bisects PQ.

Hence proved.