Angle Bisector And Its Construction

Before talking about an angle bisector, let us quickly recall the types of angles. Depending on the inclination between the two arms, an angle may be acute (less than 90-degrees, say 60-degree angle), obtuse (more than 90-degrees) or right angle (exactly 90-degrees). Constructing angles is an important part of geometry as this knowledge is extended for construction of other geometric figures as well, primarily the triangles. A number of angles can be constructed simply by bisecting some common angles.

What is an Angle Bisector?

Also known as the bisector of an angle, it is a line that divides an angle into two equal parts. Every angle has an angle bisector. It is also the line of symmetry between the two arms of an angle, the construction of which enables you to construct smaller angles. Say you are required to construct an 30 degree angle. This can be performed by creating an 60 degree angle and then bisect it. Similarly, 90-degree, 45-degree, 15-degree and other angles are constructed using this concept.

How to Construct an Angle Bisector?

You require a ruler and a compass to construct angles and their bisectors. Given a known or unknown ∠PQR, the steps to construct its angle bisector are:

Angle Bisector

  • Step 1 : Place the compass pointer at Q and make an arc that cuts the two arms of the angle at two different points.

Angle Bisector

  • Step 2: From the point where the first arc cut the arm QP, make another arc towards the interior of the angle.

Angle Bisector

  • Step 3: Without changing the radius on the compass, repeat step 2 from the point where the first arc cut QR.

Angle Bisector

  • Step 4: Using a ruler, draw a line from Q to the point where the arcs intersect.

Angle Bisector

The line that was drawn through Q represents the angle bisector of the ∠PQR.

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Practise This Question

Draw a line AB. At A, draw an arc of length 3cm using compass such that it intersects AB at O. With the same spread of compass, put the compass pointer at O and make an arc that intersects the previous arc at P. With the same spread again, put the compass pointer at P and draw an arc that intersects the first arc at Q. Join A and Q. Using the protractor, measure QAB. What is the value of QAB.