Definition:Bisection/Bisector

Definition

A bisector is an object which bisects another object.

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

Let $AB$ be a line segment.

The perpendicular bisector of $AB$ is the straight line which:

passes through the point which bisects $AB$.

Let $L = AB$ be a line segment whose endpoints are $A$ and $B$.

Let $M$ be a point on $L$ such that the line segment $AM$ is equal to the line segment $MB$.

That is, let $M$ be the bisector of $L$.

Then $M$ is the midpoint of $L$.