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?

Given: (i) P is parallel to line l

To construct: a parallel line through R

Steps for construction

Step 1 : We have to draw a line l with point P not on line l .

Step 2 : We have to take a point B on line l an join them and then we have to draw an arc taking b as center , cutting l at C and PB at D

Step 3 : Taking the same radius we have to draw an arc with P as center and intersecting PB at E.

Step 4: We have to measure the length of CD using the compass and draw an arc taking E as center and cutting at F.

Step 5 : We have to draw a line m passing through P and F. Line l and m are parallel.

Step 6 : We have taken any point R on m and any point Q on l and join PQ.

Step 7 : Taking P as center , we will draw an arc intersecting line PQ at G and line m at H

Step 8 : We have to consider the same radius as before and taking R as center , we will draw an arc intersecting line m at I.

Step 9: We have to measure the length of GH using the compass and draw an arc taking I as center and cutting at K. We will draw a line joining R and K and intersecting line l at S

Now PQ is parallel to RS andd line l is parallel to line m

Therefore we can say that it is a parallelogram.