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:
\begin{itemize}
\item The \PMlinkname{measure}{AngleMeasure} of any interior angle of a regular hexagon is $120^{\circ}$.
\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 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}
From the last remark, it is easy to see that a regular hexagon is constructible by ruler and straightedge. |
