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?

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?

Philoid · Accepted Answer

We have to draw figure using following steps of construction:

Step 1: Draw a line l and mark one-point A on the line l and the other point P above the line l.

Step 2: With A as a center and a certain radius draw an arc intersecting l at B and AP at C.

Step 3: Now, with the same radius taking the center as P draw an arc DE cutting AP at F.

Step 4: Adjust the compasses according to the length of BC. And with same opening, taking F as a center, draw another arc intersecting the previous arc DE at point G.

Step 5: Now, join PG to draw a line m which will be parallel to line m

Step 6: Now, join P to Any random point Q on the line l.

Step 7: Then choose another point R on line m. Similarly, a point we can draw a line through R which would be parallel to PQ.

Hence, extend it to meet line l at point S.

∴In quadrilateral PQRS opposite lines are parallel to each other.

And PQRS is a parallelogram.