Angle Bisector

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

In the figure, the ray KM bisects the angle JKL .

The angles JKM and LKM are congruent.

So, mJKM=mLKM .

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, BD is an angle bisector. Find the measure of ABC .

Since BD is an angle bisector,

mCBD=mABD

Therefore,

mCBD=65°

By the Angle Addition Postulate,

mABC=mABD+mCBD .

Substitute.

mABC=65°+65° =130°