Question

Let $l$ be a line and $P$ be a point not on $l$. Through $P$, draw a line $m$ parallel to $l$. Now join $P$ to any point $Q$ on $l$. Choose any other point $R$ on $m$. Through $R$, draw a line parallel to $PQ$. Let this meet $l$ at $S$. What shape do the two sets of parallel lines enclose?

Answer 1

Follow the steps given in question for constructing the figure:

In figure, $PR\parallel SQ$ and $PQ\parallel SR$

In $\mathrm{PQRS}$ opposite sides are parallel so they form a parallelogram.

Hence, a parallelogram $PQRS$ is enclosed between line $m$ and $l$.