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Practice Time 15B

1. With the help of a ruler and a pair of compasses, construct the following angles.
1 °
(a) 60° (b) 30° (c) 90° (d) 22 2
2. Draw an angle of 140°. Bisect it using a pair of compasses.

3. Draw an angle of 105° and find its bisector.
4. Draw ∠AOB. Take a point P on arm OA and point Q on arm OB such that OP = OQ. Draw perpendicular
bisectors of OP and OQ. Let them meet at M. Is PM = MQ?
5. Construct ∠AOB = 128° with the help of a protractor and bisect the angle using a ruler and a pair of
compasses.
6. Draw ∠AOB = 75° with the help of a protractor. Draw a line segment PQ = 4.2 cm and construct an
angle ∠RPQ = ∠AOB with a ruler and pair of compasses.

Construction of Parallel Lines

We know that lines that do not intersect one another, even when extended indefinitely in both
directions, are called parallel lines.

When two such parallel lines are intersected by a transversal, then the corresponding angles
and alternate interior angles formed are equal. Conversely, when two lines are intersecting by a
transversal and alternate interior angles (or corresponding angles) are equal, then the lines are

parallel. We shall use these facts to construct parallel lines.
Construction of a Line Parallel to a Given Line Through a Point Outside the Line

Let us construct a line parallel to a given line through a point lying outside the line.

The construction can be done using the fact that alternate angles are equal if lines are parallel.

Steps of construction:
1. Draw a line AB and a point X outside the line.
2. Take any point P on line AB. Join XP. G F X H

3. With P as centre and any radius, draw an arc to cut
AB at C and PX at D. E
4. With X as centre and the same radius as before, D
draw an arc cutting PX at E.
A P C B
5. With E as centre and radius equal to CD, draw an
arc to cut the previous arc at F.

6. Join XF and produce it on both sides to get the required line GH parallel to AB.

Verify: ∠CPD and ∠FXE are alternate interior angles. We constructed angles such that

∠CPD = ∠FXE. Since alternate angles are equal, so lines AB and GH are parallel, i.e., AB GH
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