What is a Bisector? Definition and Examples

A bisector of a line segment is a line that divides the segment into two equal parts. In other words, it is a line that passes through the midpoint of the segment and has the same length as the segment.

For example, if we have a line segment AB, then a bisector of AB is a line that passes through the midpoint M of AB and has the same length as AB. The point M is the midpoint of AB, so the bisector of AB is the line that passes through M and has the same length as AB.

Bisectors are used in many geometric constructions and proofs, such as proving that two lines are parallel or perpendicular, or finding the midpoint of a line segment. They are also used in algebra to solve equations and inequalities, and in calculus to find extrema and optimize functions.