Question

If p and q are points of trisection of the diagonal bd of a parallelogram abcd, prove that cq || ap​

Answer 1

Answer:

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}

Step-by-step explanation:

please mark me brilliant ❤️

Answer 2

Answer:

Given :

• ABCD is a parallelogram
• BD and AC are diagonal of it

To Find :

• CQ || AP

Solution :

As we know,

Diagonals of a parallelogram bisects each other

→ OA = OC

→ OB = OD

Since P and Q are points of trisection of BD

∴ BP = PQ = QD

Now,

→ OB - BP = OD - QD

→ OP = OQ

In quadrilateral APCQ

→ OA = OC

→ OP = OQ

Diagonals of quadrilateral APCQ bisects each other.

∴ APCQ is a parallelogram

• Opposite sides are parallel of a parallelogram

∴ AP || CQ

Hence, proved.