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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?

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Solution

To construct: A pair of parallel lines intersecting other pair of parallel lines.
Steps of construction:

(a) Draw a line l and take a point P outside of l .
(b) Take point Q on line l and join PQ.
(c) Make equal angle at point P such that Q=P.
(d) Extend line at P to get line m.
(e) Similarly, take a point R on line m, at point R, draw angles such that P=R.
(f) Extended line at R which intersects at S on line l. Draw line RS. Thus, we get parallelogram PQRS.


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