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 pair 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 on line m, at point R, draw angles such that $\angle P=\angle R$.
(f) Extended line at R which intersects at S on line l. Draw line RS. Thus, we get parallelogram PQRS.