Question

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

Answer 1

Answer:

In ∆DPC and BQA,

DP=BQ (given)

AB=CD ( ABCD is a parallelogram)

angle CDP = angle ABQ

∆DPC=~∆ BQA

Therefore, AB= AQ

Similarly, AP= CQ

Therefore, APCQ is a parallelogram.

Hence, PQ and AC bisect each other.

Hope it helps you.