# Equiangular Triangle

A triangle which has all three interior angles equal (congruent).
Try this Drag the orange dots on each vertex to reshape the triangle. Notice it always remains an equiangular triangle. The angles A,B and C always remain equal in measure.

An equiangular triangle is a triangle where all three interior angles are equal in measure. Because the interior angles of any triangle always add up to 180°, each angle is always a third of that, or 60°

The sides of an equiangular triangle are all the same length (congruent), and so an equiangular triangle is really the same thing as an equilateral triangle. See Equilateral Triangles.

## Properties

• All three sides of an equiangular triangle are congruent (same length).
• The area of an equiangular 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.
• For an equiangular triangle, the radius of the incircle is exactly half the radius of the circumcircle.

## Constructing an Equiangular Triangle

It is possible to construct an equiangular triangle of a given side length using just a compass and straightedge. This uses the same method as for an equilateral triangle, see Constructing an Equilateral Triangle