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? [4 MARKS]

Answer 1

Steps: 2 Marks
Construction: 2 Marks

To construct: A pair of parallel lines intersecting other parts of parallel lines.

Steps of construction:

Draw a line l and take a point P outside l.

Take point Q on line l and join PQ.

Make equal angle at point P such that $\angle Q=\angle P$.

Extend line at P to get line m.

Similarly, taking a point R on line m, at point R, draw angles such that $\angle P=\angle R$.

The extended line at R which intersects at S on line l, Draw line RS. Thus, we get a parallelogram PQRS.