equilateral triangle

An equilateral triangle is one for which all 3 sides are congruent.

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

• It is a regular polygon.

• The bisector of any angle coincides with the height, the median and the perpendicular bisector of the .

• 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	equilateral triangle
Canonical name	EquilateralTriangle
Date of creation	2013-03-22 11:44:04
Last modified on	2013-03-22 11:44:04
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	22
Author	Mathprof (13753)
Entry type	Definition
Classification	msc 51-00
Classification	msc 81-00
Classification	msc 08-01
Related topic	Triangle
Related topic	IsoscelesTriangle
Related topic	EquivalentConditionsForTriangles
Related topic	EquiangularTriangle
Related topic	RegularTriangle