equiangular triangle

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


By the theorem at determining from angles that a triangle is isosceles, we can conclude that, in any geometryMathworldPlanetmathPlanetmath in which ASA holds, an equilateral triangleMathworldPlanetmath is regularPlanetmathPlanetmathPlanetmath (http://planetmath.org/RegularTriangle). In any geometry in which ASA, SAS, SSS, and AAS all hold, the isosceles triangle theorem yields that the bisectorMathworldPlanetmath 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 r32.

  • If r is the length of the side, then the area is equal to r234.

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