Question

PQRS is a parallelogram and M, N are the mid-points of PQ and RS respectively. Which of the following is not true ?

• A. RM trisects QS
• B. PN trisects QS
• C. $\Delta$PSN $\sim$ $\Delta$QMR
• D. MS is not parallel to QN

Answer 1

The correct option is D MS is not parallel to QN

In parallelogram $PQRS,$

We know that $PQ=SR$

Given, M is the mid-point of PQ and N is the mid-point of RS

$\therefore PM=MQ=SN=NR$ ...(1)

and we know that sides$PQ$ and $RS$ are parallel to each other.
$\therefore QM$ and $NS$ will also be parallel to each other.

$\therefore$ We can say that $MSNQ$ is a parallelogram
Hence its opposite sides will also be parallel

$\Rightarrow MS\parallel QN$

option D is incorrect so the correct answer according to the question is Option D.