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