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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

Therefore,

m ∠ C B D = 65 °

By the Angle Addition Postulate,

m ∠ A B C = m ∠ A B D + m ∠ C B D .

Substitute.

m ∠ A B C = 65 ° + 65 °                                         = 130 °