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.

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More Geometric Constructions & Geometry Lessons

The following diagram shows the perpendicular bisector of the line segment AB. Scroll down the page for examples and step-by-step solutions on how to construct a perpendicular bisector.

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

How to construct a perpendicular bisector?

Example:

Construct a perpendicular bisector of the given line segment AB.

Solution:

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.

How to construct an isosceles triangle or a rhombus?

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

Example:

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

How to construct a perpendicular bisector of a line segment?

How to bisect a line segment using only a compass and straightedge?

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.

The circumcenter is the point of concurrency for the perpendicular bisectors of the sides of a triangle.

The circumcenter is the center of a circle that passes through the vertices of the triangle. The circumcenter is equidistant to the vertices.

We say the circle circumscribes the triangle.

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