Abcd is a parallelogram whose diagonals intersect at o.P is the point on diagonal ac such that pa:ao=1:2
Answers
Answer:
Given : ABCD is a parallelogram. AC and BD are the diagonals of the parallelogram which intersect at point O and points P and Q trisects the diagonal BD.
Construction: Join A to Q and P, Join C to Q and P
To Prove: CQIIAP and AC bisects PQ means OP = OQ
Proof: Diagonals AC and BD of a parallelogram bisect each other at O.
So, OB = OD and OC = OA
Now, P and Q trisect the diagonal BD where trisect means divide something in three equal parts.
So, DQ = PQ = BP
OB = OD
BP +OP = DQ +OQ
OP = OQ (because BP is already equal to DQ)
Thus, in quadrilateral APCQ, diagonal AC and PQ are such that OP = OQ and OA = OC
So, the diagonal AC and PQ bisect each other.
And if the diagonal of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Therefore, APCQ is a parallelogram.
So, CQ || AP
Hence Proved
please mark this as a brainliest answer