Equilateral Polygon is not necessarily Equiangular

Theorem

Let $P$ be an equilateral polygon with more than $3$ sides.

Then it is not necessarily the case that $P$ is also equiangular.


Proof

Proof by Counterexample

We take as an example the rhombus:


A rhombus is a parallelogram whose sides are all the same length.

Its angles may or may not all be equal.

$\blacksquare$


Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): polygon
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): polygon
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