if p and q are points of trisection of the diagonal bd of a parallelogram abcd, prove that cq = ap
Answers
Answered by
11
Given ABCD is a parallelogram. AC and BD are the diagonals of the parallelogram which intersect at point O.
The points P and Q trisects the diagonal BD.
Now, since the diagonals of a parallelogram bisect each other
So, Ac and Bd bisect each other at O
=> OB = OD and OA = OC
Now, P and PQ trisect the diagonal BD
So, DQ = PQ = BP
OB = OD and BP = DQ
Now, OB - BP = OD - DQ
=> OP = OQ
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.
Again if the diagonal of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Hence, ABCD is a parallelogram.
So, CQ || AP {since sides of parallelogram are parallel}
Hope it is helpful.
Similar questions