Angle bisector

An angle bisector is a ray that divides an angle into two congruent angles or two angles that have the same measure.

For example, in the figure below, ray OB shown in red is an angle bisector and it divides angle AOC into two congruent angles.

These two congruent angles are angle AOB and angle COB.

In other words, m∠AOB = m∠COB

Notice that within the ray, segment OB has the same endpoint as ray OB. Therefore,

It is perfectly ok to say that the ray or the segment bisects angle AOC.

Angle bisector

Learn how to find an angle bisector by reading this lesson.

Angle bisector of a triangle

An angle bisector of a triangle is a segment that bisects an angle of that triangle and extends to the opposite side.

Angle bisector of a triangle

In triangle ABC shown above, segment CE is an angle bisector for that triangle.

Segment CE bisects angle ACB and creates angle ACE and angle BCE that are congruent.

In other words, m∠ACE = m∠BCE

You could also say that m∠e = m∠f

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