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'equilateral triangle'
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| Title of object: |
equilateral triangle |
| Canonical Name: |
EquilateralTriangle |
| Type: |
Definition |
| Created on: |
2001-10-06 17:57:14 |
| Modified on: |
2007-06-19 09:33:26 |
| Classification: |
msc:51-00 |
| Keywords: |
Triangle |
Revision comment (for changes between this and next version):
| Changes for correction #12499 ('picture is not displaying'). |
Preamble:
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{xypic}
\usepackage{pstricks} |
Content:
An \emph{equilateral triangle} is one for which all 3 sides are congruent.
\begin{center}
\begin{pspicture}(-0.2,-0.2)(5.2,5.2)
\pspolygon(0,0)(5,0)(2.5,4.33)
\rput[b](2.5,4.5){A}
\rput[a](0,-0.2){B}
\rput[a](5,-0.2){C}
\psline(2.5,-0.2)(2.5,0.2)
\psline(1.15,2.2)(1.35,2.1)
\psline(3.65,2.1)(3.85,2.2)
\end{pspicture}
\end{center}
The following statements hold in Euclidean geometry for an equilateral triangle.
\begin{itemize}
\item
It is a regular polygon.
\item
The bisector of any angle coincides with the height, the median and the perpendicular bisector of the \PMlinkescapetext{opposite side}.
\item
If $r$ is the length of the side, then the height is equal to $\displaystyle \frac{r\sqrt{3}}{2}$.
\item
If $r$ is the length of the side, then the area is equal to $\displaystyle \frac{r^2\sqrt{3}}{4}$.
\end{itemize} |
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