Angle Bisector of a Plane Angle

Theorem: Angle Bisector of a Plane Angle

Let $\angle (a;b)$ be the plane angle formed by two rays $a$ and $b$.

There exists one and only one straight line $l$ in the plane of $\angle (a;b)$ which goes through the vertex of $\angle (a;b)$ such that the angles $\angle (a;l)$ and $\angle (l;b)$ are congruent.

PROOF

TODO

Definition: Angle Bisector of a Plane Angle

The angle bisector of a plane angle is the unique straight line which lies in the plane of the angle, goes through its vertex and divides it into two congruent angles.