regular triangle
A regular triangle is one for which all sides are congruent and all interior angles^{} are congruent.
All regular triangles are regular polygons^{}. Also, by the isosceles triangle theorem, the bisector^{} of any angle coincides with the height, the median and the perpendicular bisector of the opposite side.
The following statements hold in Euclidean geometry^{} for a regular triangle.

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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  regular triangle 
Canonical name  RegularTriangle 
Date of creation  20130322 17:12:52 
Last modified on  20130322 17:12:52 
Owner  Wkbj79 (1863) 
Last modified by  Wkbj79 (1863) 
Numerical id  6 
Author  Wkbj79 (1863) 
Entry type  Definition 
Classification  msc 5100 
Related topic  Triangle 
Related topic  IsoscelesTriangle 
Related topic  EquilateralTriangle 
Related topic  EquiangularTriangle 
Related topic  EquivalentConditionsForTriangles 
Related topic  RegularPolygon 