Equilateral Triangle

A triangle which has all three of its sides equal in length.

Try this Drag the orange dots on each vertex to reshape the triangle. Notice it always remains an equilateral triangle. The sides AB, BC and AC always remain equal in length

An equilateral triangle is one in which all three sides are congruent (same length). Because it also has the property that all three interior angles are equal, it really the same thing as an equiangular triangle. See Equiangular triangles.

An equilateral triangle is simply a specific case of a regular polygon, in this case with 3 sides. All the facts and properties described for regular polygons apply to an equilateral triangle. See Regular Polygons

Properties

All three angles of an equilateral triangle are always 60°. In the figure above, the angles ∠ABC, ∠CAB and ∠ACB are always the same. Since the angles are the same and the internal angles of any triangle always add to 180°, each is 60°.
The area of an equilateral triangle can be calculated in the usual way, but in this special case of an equilateral triangle, it is also given by the formula: where S is the length of any one side. See Area of an equilateral triangle.
With an equilateral triangle, the radius of the incircle is exactly half the radius of the circumcircle.

Constructing an Equilateral Triangle

It is possible to construct an equilateral triangle of a given side length using just a compass and straightedge. See Constructing an Equilateral Triangle

Equilateral Triangle

Properties

Constructing an Equilateral Triangle

Other triangle topics

General

Perimeter / Area

Triangle types

Triangle centers

Congruence and Similarity

Solving triangles

Triangle quizzes and exercises