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. $QL=2QN$
• B. $QL=2QR$
• C. $QL=PL$
• D. $QL=PQ$

Answer 1

The correct option is A $QL=2QN$

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] ---------(1)

Given, ABCD is parallelogram

$\therefore$ SR || PQ or SN || PQ [Opposite sides of a parallelogram are parallel]

In $△$LPQ, S is the mid point of PL (from 1) and SN || PQ.

$\therefore$ N is the mid point of QL [converse of mid-point theorem]

$\Rightarrow QL=2QN$