An angle bisector divides an angle into two equal angles. If the angle is x°, each of the two angles formed will now be x/2°. The angle bisector passes through the vertex of the angle. The figure below shows an angle bisector of angle ABC.

Angle bisector

For Example: Angle ABC is 120° angle. BD is the angle bisector. What will be the measure of angles ABD and DBC?

ABD= DBC = 120/2 = 60° each

 

 

Construction of Angle Bisector

 

An angle bisector can be constructed using a compass. Let us bisect the angle ABC. Following are the steps to draw an angle bisector:

1. With the center A, draw an arc cutting both the rays of the angle as shown in the figure. The arc is cutting the rays AB and AC at P and Q respectively.

Construction Of Angle Bisector

2.  Taking P and Q as centers draw 2 arcs cutting each other at a point X.

Construction Of Bisector of an angle

3. Draw a line passing through vertex B and the point X.

bisector of an angle

4. BD is the required angle bisector of the angle ABC.

  

Angle Bisectors in a Triangle

 

The angle bisectors of the three angles of a triangle intersect at a point. This point is called as the incentre of the triangle. A circle that is drawn inside the triangle with 'incentre' as the centre is called as the inscribed circle. The perpendicular distance of this point from all the sides is same and it is the radius of the circle.

Angle Bisectors in a Triangle

I is the point of intersection of the angle bisectors in the triangle shown above and it is called as the incentre of the triangle.