question_answer 3)

Let I be a line and P be a point not on I. 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 I at S. What shape do the two sets of parallel lines enclose? 

Answer:

                Steps of Construction    1. Draw a line l and a point P not on it.            2. Take any point A on l. 3. Join A to P. 4. With A as centre and a convenient radius, draw an arc cutting I at B and AP at C. 5. Now with P as centre and the same radius as in step 4, draw an arc DE cutting PA at T. 6. Place the pointed tip of the compasses at B and adjust the opening so that the pencil tip is at C. 7. With the same opening as in step 6 and with T as centre, draw an arc cutting the arc DE at F. 8. Now just PF to draw a line m. Then line \[m||\] line I. 9. Join P to any point Q on I. 10. Choose any point R on m. 11. Join R to Q. 12. With Q as centre and a convenient radius, draw an arc cutting PQ at L and RQ at M. 13. Now with R as centre and the same radius as in step 12, draw an arc GH cutting PQ at I. 14. Place the pointed tip of the compasses at L and adjust the opening so that the pencil tip is at M. 15. With the same opening as in step 14 and with I as centre, draw an arc cutting the arc GH at J. 16. Now join RJ to draw a line n. Then line \[n||\] line PQ. Let the line n meet the line l at S. Then, the shape enclosed by the two sets of parallel lines is a parallelogram.