Definition:Angle Bisector



Let $\angle ABC$ be an angle.

The angle bisector of $\angle ABC$ is the straight line which bisects $\angle ABC$.

In the above diagram, $BD$ is the angle bisector of $\angle ABC$.

Thus $\angle ABD \cong \angle DBC$ and $\angle ABD + \angle DBC = \angle ABC$.

Note
The construction of an angle bisector is Proposition 9 of Book I of Euclid's.