Definition:Angle Bisector
From ProofWiki
Definition
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 $\angle ABD + \angle DBC = \angle ABC$.
Also see
The construction of an angle bisector is Proposition 9 of Book I of Euclid's The Elements.
