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Revision difference : hexagon |
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Version 5 |
| An \emph{hexagon} is a $6$-sided polygon. The most commonly quoted hexagon is a regular hexagon, having congruent sides and congruent interior angles. Below is an example of a regular hexagon: |
An \emph{hexagon} is a $6$-sided polygon. The most commonly quoted hexagon is a regular hexagon, having congruent sides and congruent interior angles. Below is an example of a regular hexagon: |
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| Below are some properties of regular hexagons in Euclidean geometry: |
Below are some properties of regular hexagons in Euclidean geometry: |
| \begin{itemize} |
\begin{itemize} |
| \item The \PMlinkname{measure}{AngleMeasure} of any interior angle of a regular hexagon is $120^{\circ}$. |
\item The \PMlinkname{measure}{AngleMeasure} of any interior angle of a regular hexagon is $120^{\circ}$. |
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\item The smallest $n$ for which a non-degenerate regular $n$-gon has diagonals which are not congruent is $n=6$. For example, in the regular hexagon below, the diagonal drawn in blue and the one drawn in red are not congruent.
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\item The smallest $n$ for which no pairs of diagonals of an arbitrary non-degenerate regular $n$-gon are congruent is $n=6$. For example, in the regular hexagon below, the diagonal drawn in blue and the one drawn in red are not congruent.
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\begin{center} |
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\psline[linecolor=red](4.5,0)(1.5,5.196) |
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| \item The side of a regular hexagon has the same length as the radius of the circle circumscribing it. This fact is illustrated below. |
\item The side of a regular hexagon has the same length as the radius of the circle circumscribing it. This fact is illustrated below. |
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| \end{itemize} |
\end{itemize} |
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