Question

M is the mid point of side PQ of a parallelogram PQRS. A line through Q parallel to MS meets SR at N and PS produced at L.



Then which of the following is correct?

• A. $PL=QR$
• B. $PL=2QR$
• C. $PL=3QR$
• D. $PL=MS$

Answer 1

The correct option is B $PL=2QR$

In $△$PLQ, M is the mid point of PQ and MS ||QL

$\therefore$ S is the mid point of PL [converse of mid-point theorem]

$\Rightarrow PL=2PS$

Given, PQRS is a parallelogram.

Since, in parallelogram opposite sides are parallel and equal.

Therefore, PS = QR

$\Rightarrow PL=2QR$