Question

M is the midpoint of side PQ of a parallelogram PQRS. A line through Q parallel to MS meets SR at N and PS produced at L. Prove that QL = 2QN.

Answer 1

In triangle 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, PQRS is parallelogram

therefore SR || PQ or SP || QR [Opposite sides of a parallelogram are parallel]

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

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

$\Rightarrow QL=2QN$