# 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?

**Solution:**

We use the basic rules of construction to solve the question given.

Let's follow the steps given below.

**Steps of construction:**

- Draw a line l, take a point A on it.
- Take a point P, not on l and join A to P.
- Taking A as a centre and with a convenient radius draw an arc cutting l at B and AP at C.
- Taking P as the centre and with the same radius as before, draw an arc DE to intersect AP at F.
- Adjust the compass up to the length of BC and without changing the opening of compass and taking F as the centre, draw an arc to intersect the previous drawn arc DE at point G.
- Join P to point G to draw a line m. Line m will be parallel to l.
- Join P to any point Q on line l. Choose another point R on line m.
- Similarly, a line can be drawn through point R and parallel to PQ using the above steps. Let it meet line l at point S.
- Thus, line PQ is parallel to RS.

The shape enclosed by these two sets of parallel lines is a parallelogram PQRS with PR || QS and PQ || RS.

**ā Check: **NCERT Solutions Class 7 Maths Chapter 10

**Video Solution:**

## 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?

Class 7 Maths NCERT Solutions Chapter 10 Exercise 10.1 Question 3

**Summary:**

l is a line and P is a point not on l. Through P, a line m is drawn parallel to l. Point P is joined to point Q on l. Another point R is chosen on m. Through R, a line is drawn parallel to PQ. The shape enclosed by these two sets of parallel lines is a parallelogram PQRS with PR || QS and PQ || RS.

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