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Angle Bisector

An angle bisector is a line or ray that divides an angle into two congruent angles .

In the figure, the ray K M bisects the angle J K L .

The angles J K M and L K M are congruent.

So, m J K M = m L K M .

Note that any point on the angle bisector is equidistant from the two sides of the angle. Some textbooks call this Angle Bisector Theorem , but this name is usually used for another theorem about angle bisectors in a triangle.


Example :

In the figure, B D is an angle bisector. Find the measure of A B C .

Since B D is an angle bisector,

m C B D = m A B D


m C B D = 65 °

By the Angle Addition Postulate,

m A B C = m A B D + m C B D .


m A B C = 65 ° + 65 ° = 130 °