Definition:Angle Bisector

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 $\angle ABD + \angle DBC = \angle ABC$.

Internal

Let $\angle APB$ be an angle.

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

In the above diagram, $PC$ is the internal angle bisector of $\angle APB$.

Thus $\angle APC \cong \angle BPC$ and $\angle APC + \angle BPC = \angle APB$.

External

Let $\angle APB$ be an angle.

Let $BP$ be produced beyond $P$ to $B'$.

The external angle bisector of $\angle APB$ is the straight line which bisects $\angle APB'$.

In the above diagram, $PD$ is the external angle bisector of $\angle APB$.

Thus $\angle APD \cong \angle B'PD$ and $\angle APD + \angle B'PD = \angle APB'$.

Also known as

The angle bisector of an angle can also be referred to just as the bisector if the angular nature of its object is understood.

An older term for the same thing is bisectrix.

Also see

• Euclid's The Elements: Proposition $9$ of Book $\text{I} $: Bisection of Angle.

• Results about angle bisectors can be found here.

Source

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): bisect
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): bisect
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): bisector