• Home
• /
• Blog
• /
• How to Construct a Perpendicular Bisector(With Steps & Examples)

# How to Construct a Perpendicular Bisector(With Steps & Examples)

December 7, 2022

This post is also available in: हिन्दी (Hindi)

A perpendicular bisector is a straight line that is at a right angle with a given line or makes an angle of $90^{\circ}$ with another line and bisects (divides into two equal parts) it. Perpendicular bisectors are frequently used in geometry, especially in triangles, and have wide applications.

Let’s understand how to construct a perpendicular bisector with steps and examples.

## Properties of a Perpendicular Bisector

The following are the important properties of a perpendicular bisector.

• Divides a line segment or a line into two congruent segments.
• Divides the sides of a triangle into congruent parts.
• They make an angle of 90° with the line that is being bisected.
• They intersect the line segment exactly at its midpoint.
• The point of intersection of the perpendicular bisectors in a triangle is called its circumcenter.
• In an acute triangle, they meet inside a triangle, in an obtuse triangle they meet outside the triangle, and in right triangles, they meet at the hypotenuse.
• Any point on the perpendicular bisector is equidistant from both ends of the segment that they bisect.
• Can be only one in number for a given line segment.

## How to Construct a Perpendicular Bisector of a Segment?

Perpendicular bisector on a line segment can be constructed easily using a ruler and a compass. The constructed perpendicular bisector divides the given line segment into two equal parts exactly at its midpoint and makes two congruent line segments.

### Steps for Constructing Perpendicular Bisector

The following steps are used to construct a perpendicular bisector of a line segment.

Step 1: Draw a line segment $\text{AB}$ of any suitable length.

Step 2: Take a compass, and with $\text{A}$ as the centre and with more than half of the line segment $\text{AB}$ as width, draw arcs above and below the line segment.