# Perpendicular Bisector: Definition & Theorem

## What is a perpendicular bisector?

A perpendicular bisector of a line segment is a line that passes through the mid point of the line segment and is perpendicular to the line.

## How do you draw a perpendicular bisector?

To draw a perpendicular bisector you need the following things :

- Compass
- Sharpened Pencil
- Ruler

### Instructions :

- Draw a line of any length on a piece of blank paper.
- Insert the pencil in the compass and extend the compass so its points are more than half the length of the line.
- Put the pointy end of the compass down on one end of the line segment, then use the pencil inside the compass to draw an arc over the midpoint of the line segment on both sides of the line segment.
- Now, keeping the compass exactly the way it is, put the pointy end down on the other end of the line segment and draw two more arcs over the midpoint. You will see on both sides of the line: the arcs will intersect.
- Then take a ruler and draw a line between the two intersecting points that will pass through the line segment. This line is your perpendicular bisector.

## Perpendicular bisector of a triangle

Perpendicular bisectors of triangles are drawn at each side of the triangle. Thus each triangle has three perpendicular bisectors. The point where the perpendicular bisectors of the triangle meet is known as the circumcenter of the triangle.

## Perpendicular bisector theorem

- The theorem states that if a point is on the perpendicular bisector of a line segment, then that point is at an equal distance from both endpoints of the line segment.
- The converse of the perpendicular bisector theorem states that if a point is at an equal distance from both ends of a line segment, then that point lies on the perpendicular bisector of that line segment.

### Why are perpendicular bisectors useful?

Perpendicular bisectors are useful in geometry, if we want to find a mid point of distances. This is necessary in architecture and study of mechanics and machinery and their construction.