equiangular triangle

An equiangular triangle is one for which all three interior angles are congruent.

By the theorem at determining from angles that a triangle is isosceles, we can conclude that, in any geometry in which ASA holds, an equilateral triangle is regular (http://planetmath.org/RegularTriangle). In any geometry in which ASA, SAS, SSS, and AAS all hold, the isosceles triangle theorem yields that the bisector of any angle of an equiangular triangle coincides with the height, the median and the perpendicular bisector of the opposite side.

The following statements hold in Euclidean geometry for an equiangular triangle.

• The triangle is determined by specifying one side.

• If $r$ is the length of the side, then the height is equal to ${\displaystyle \frac{r\sqrt{3}}{2}}$.

• If $r$ is the length of the side, then the area is equal to ${\displaystyle \frac{r^2\sqrt{3}}{4}}$.

Title	equiangular triangle
Canonical name	EquiangularTriangle
Date of creation	2013-03-22 17:12:50
Last modified on	2013-03-22 17:12:50
Owner	Wkbj79 (1863)
Last modified by	Wkbj79 (1863)
Numerical id	8
Author	Wkbj79 (1863)
Entry type	Definition
Classification	msc 51-00
Related topic	Triangle
Related topic	IsoscelesTriangle
Related topic	EquilateralTriangle
Related topic	RegularTriangle
Related topic	EquivalentConditionsForTriangles