Page 206 - Start Up Mathematics_7

Solution: Steps of Construction:

1. Draw a line l and take a point P on it. P l

2. Place the pointed tip of the compass at
P and draw a semi-circular arc cutting Q P R l
line l at Q and R.

3. With a slightly bigger opening, mark two arcs X
from Q and R as centres cutting each other at
S. Join PS to make a perpendicular.

4. With P as centre, cut an arc of radius 2.5 cm S
to obtain a point X on the perpendicular. Q P R l

5. Repeat the above steps to draw a line perpendicular to PX at the point X.

m
X

l
P
Example 2: 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: Steps of Construction: P

1. Repeating the steps of previous
example, we construct a line m
passing through P and parallel l
to l.
D P E R m
2. With point R on line m as centre, C F
draw an arc with the same
opening as the previous arcs to B
cut line m at E. Now with CD as Q A l
arc length and E as centre, cut
the arc at F. D P E R m

3. Join RF and extend it to cut line C F
l at S.
It is clear that the two pairs B
of parallel lines enclose a Q A S l

parallelogram.

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