Question

If P and Q are points of trisection of the diagonal BD of a parallelogram ABCD, $CQ\parallel AP.$

• A. True
• B. False

Answer 1

The correct option is A True

We know that, diagonals of a parallelogram bisect each other.

$\Rightarrow$ $OA=OC$ and $OB=OD$

Since $P$ and $Q$ are point of trisection of $BD$

$\therefore$ $BP=PQ=QD$

Now, $OB=OD$ and $BP=QD$

$\Rightarrow$ $OB-BP=OD-QD$

$\Rightarrow$ $OP=OQ$

In quadrilateral $APCQ$, we have

$OA=OC$ and $OP=OQ$

Diagonals of quadrilateral $APCQ$ bisect each

$\therefore$ $APCQ$ is a parallelogram.

$\Rightarrow$ $AP\parallel CQ$ [ Opposite sides are parallel in parallelogram ]