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Basic Constructions

In earlier classes you might have learnt to construct perpendicular bisector of a line segment, angles of 300,450 600, 900, 1200 and also to draw bisector of the given angle. An angle bisector is a ray, which divides an angle in to two equal parts.  A line bisector is a line that cuts a line segment into two equal halves. A perpendicular bisector is a line, which divides a given line segment into two equal halves and is also perpendicular to the line segment.

To construct the bisector of a given angle.
Let’s consider angle DEF, we want to construct the bisector of angle DEF.
Steps of construction:

1. With E as centre and small radius draw arcs on the rays DE and EF.

2. Let the arcs intersect the rays DE and EF at G and H respectively.

3. With centres G and H draw two more arcs with the same radius such that they intersect at a point . Let the intersecting point be I

4. Now draw a ray with E as the starting point passing through I

5. EI is the bisector of the angle DEF

To construct a perpendicular bisector of a line segment
Lets consider the line segment as PQ. We have to construct the perpendicular bisector of PQ.
Steps of Construction:

1. Draw a line segment PQ.

2. With P as centre draw two arcs on either sides of PQ with radius more the half the length of the given line segment.

3. Similarly draw two more arcs with same radius from point Q such that they intersect the previous arcs at R and S respectively.

4. Join the Points R and S.  RS is the required perpendicular bisector of the given line segment PQ.

To Construct an angle of 600 at the initial point of a given ray.
Let us take ray PQ with P as the initial point. We have to construct a ray PR such that it makes angle of 600 with PQ.
Steps of Constructions:

1. Draw a ray PQ

2. With P as centre draw an arc with small radius such that it intersects ray PQ at C.

3. With C as centre and same radius draw another arc to intersect the previous arc at D.

4. Draw a ray PR from point P through D. Hence the angle RPQ is equal to 60 degrees.