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Construct A Perpendicular Bisector

In these lessons, we will learn how to construct the perpendicular bisector of a line segment using a compass and a straightedge or ruler. We will also learn how a perpendicular bisector can be used to form a rhombus or kite and to find the midpoint of a line segment.

Related Topics: More Geometric Constructions & Geometry Lessons

The perpendicular bisector of a line segment AB is a line that divides the line AB into two equal parts at a right angle.

Example :

Construct a perpendicular bisector of the given line segment AB.


Step 1 : Stretch your compasses until it is more then half the length of AB. Put the sharp end at A and mark an arc above and another arc below line segment AB.

Step 2 : Without changing the width of the compasses, put the sharp end at B and mark arcs above and below the line segment AB that will intersect with the arcs drawn in step 1.

Step 3 : Join the two points where the arcs intersect with a straight line. This line is the perpendicular bisector of AB. P is the midpoint of AB.

The above construction steps can also be used to construct an isosceles triangle or a rhombus.

For example,

We have constructed 4 isosceles triangles; AQB, ARB, QAR and ARB. We have also constructed a rhombus AQBR.

The following video shows how to construct a perpendicular bisector of a line segment.

The following video shows how to bisect a line segment using only a compass and straightedge.

Uses of a Perpendicular Bisector

Constructing a Perpendicular Bisector with Isosceles Triangles.
Forming either a Rhombus or a Kite and then joining opposite vertices with perpendicular diagonals bisecting each other.

How to Find the Midpoint of a Line Segment Using a Perpendicular Bisector
In this tutorial about geometric constructions, we walk through how to locate the mid-point of a line segment without a ruler, using a math compass and a straightedge. We can find the mid-point by draw a perpendicular bisector.
Constructing the Perpendicular Bisectors of the Sides of a Triangle
This video explains how to construct the perpendicular bisectors of the sides of a triangle and define the properties of the perpendicular bisectors of the sides of a triangle.


Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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