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

To construct: A pair of parallel lines intersecting other part of parallel lines
Steps of construction:
(a) Draw a line $$l$$ and ,take a point $$P$$ outside of $$l$$
(b) Take point $$Q$$ on line $$l$$ and join $$PQ$$
(c) Make equal angle at point $$P$$ such that $$\angle {Q}=\angle {P}$$
(d) Extend line at $$P$$ to get line $$m$$
(e) Similarly, take a point $$R$$ online $$m$$, at point $$R$$, draw angles such that $$\angle {P}=\angle {R}$$
(f) Extended line at $$R$$ which intersects at $$S$$ online $$l$$. Draw line $$RS$$
Thus, we get parallelogram $$PQRS$$