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Opposite Basic Polygon Basic Length Geometry Angle Congruence Area Trapezoid Regular Polygon Height Of A Triangle Perpendicular Bisector Isosceles Triangle Theorem

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Regular Triangle

A regular triangle is one for which all sides are congruent and all interior angles are congruent.

$\begin{pspicture}(-0.2,-0.2)(5.2,5.2) \pspolygon(0,0)(5,0)(2.5,4.33) \rput[b](2.... ...}{60} \psarc(5,0){0.5}{120}{180} \psarc(2.5,4.33){0.5}{240}{300} \end{pspicture}$

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.

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

1	Opposite
1	Basic Polygon
1	Angle
1	Geometry
1	Basic Length
2	Area
2	Congruence
3	Regular Polygon
3	Trapezoid
4	Height Of A Triangle
4	Perpendicular Bisector
15	Isosceles Triangle Theorem