Question 3 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?
Let’s first draw a line parallel to l, passing through point P
1. Given a line l
with point P not on it
2. Mark point B on the line l
Join PB
3. With B as center, and any radius,
draw an arc
intersecting l at C, and PB at D
4. With P as center,
and same radius as before,
draw an arc intersecting PB at E
5. Open compass to length CD
6. Now, with E as center,
and compass opened the same radius as before,
draw an arc intersecting the previous arc at F
7. Draw a line m passing though P & F
Thus, m is the line parallel to l, and passing though point P
Now, our question is
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?
Let’s draw point Q on l,
and join PQ
Make a point R on m
Let’s draw point Q on l,
and join PQ
Make a point R on m
Let’s draw point Q on l,
and join PQ
Make a point R on m
Open compass to length GH
4. Now, with I as center,
and compass opened the same radius as before,
draw an arc intersecting the previous arc at K
5. Draw a line passing through R & F.
Let it intersect line l at S
So, RS is parallel to line PQ
Now, our question is
What shape do the two sets of parallel lines enclose?
Two sets of parallel lines are m & l and PQ & RS
So, the shape is PQRS
And in PQRS,
both pairs of opposite sides are parallel
∴ It is a parallelogram
Made by
Davneet Singh
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo
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