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:

1. Draw a line l, take a point A on it.
2. Take a point P, not on l and join A to P.
3. Taking A as a centre and with a convenient radius draw an arc cutting l at B and AP at C.
4. Taking P as the centre and with the same radius as before, draw an arc DE to intersect AP at F.
5. 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.
6. Join P to point G to draw a line m. Line m will be parallel to l.
7. Join P to any point Q on line l. Choose another point R on line m.
8. 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.
9. 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.

☛ 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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