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.

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The triangle is determined by specifying one side.

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

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

Canonical name  EquiangularTriangle 
Date of creation  20130322 17:12:50 
Last modified on  20130322 17:12:50 
Owner  Wkbj79 (1863) 
Last modified by  Wkbj79 (1863) 
Numerical id  8 
Author  Wkbj79 (1863) 
Entry type  Definition 
Classification  msc 5100 
Related topic  Triangle 
Related topic  IsoscelesTriangle 
Related topic  EquilateralTriangle 
Related topic  RegularTriangle 
Related topic  EquivalentConditionsForTriangles 