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Note that the equality of corresponding angles can also be used for drawing the required parallel
lines. Observe the following.

X
E
X X
E G I
D D

A P B A P C B A P C B
DPC IF
(Corresponding angles)

Construction of a Line Parallel to a Given Line at a Given Distance

Let us learn the construction of a line parallel to a given line at a given distance using the following
steps.
We will draw a line m parallel to a given line l, at a distance of 3 cm using the following steps.

Steps of Construction:
1. Let l be a given line. M N
m
2. Take any two points G and H on l. 3 cm
3. Construct perpendiculars GK and LH to l. 3 cm

4. With G as centre and radius 3 cm, cut GK at M. l
5. With H as centre and radius 3 cm, cut HL at N. G H

6. Join MN and produce it on either side to get the required line m parallel to l and at a distance
3 cm from it.

Practice Time 15C

1. Draw a line PQ. Take a point R outside it. Through R, draw a line parallel to PQ using only ruler and
compass.
2. Draw a line parallel to a given line l at a distance of
(a) 7 cm (b) 4.8 cm

3. Draw a line l. Draw a perpendicular to l at any point on it. On this perpendicular choose a point R
at 4.2 cm away from l. Through R, draw a line m parallel to l.

4. Draw a line AB. Draw a perpendicular to AB at any point on AB. On this perpendicular, choose a
point M, 4.5 cm away from AB. Through M, draw a line CD parallel to AB.

5. Draw a line LM = 6 cm. Take a point N below LM and draw a line parallel to LM and passing
through N.
Construction of Triangles

We know that every triangle has six parts – three sides and three angles. A triangle can be drawn
if any three parts, one of which is a side, are given. For construction of a triangle with given
measurements, keep the following points in mind.

345 Construction of Basic Geometrical Shapes