Question

P and Q are the points of trisection of the diagonal BD of a parallelogram ABCD. Prove that APCQ is a parallelogram.

Answer 1

Ans.
Given: P and Q are points of trisection of BD.
⇒ BP = PQ = QD
We know that diagonals of a parallelogram bisect each other
⇒ OA = OC and OB = OD
Now, OB = OD and BP = QD
⇒ OB - BP = OD - QD
⇒ OP = OQ
Thus in quadrilateral APCQ,
we have OA = OC and OP = OQ.
Since the diagonals of quadrilateral APCQ bisect each other, APCQ is a parallelogram