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Proof: By Euclid

(related to Corollary: Every Equilateral Triangle Is Equiangular.)

• If a triangle $ABC$ is equilateral, then the sides $AB$ and $BC$ have equal lengths.
• From Prop 1.05 it follows that the angles $\angle{ABC}$ and $\angle{BCA}$ are equal.
• The same follows for the angles $\angle{ABC}$ and $\angle{CAB}$, since the sides $AB$ and $AC$ are equal.
• Thus, the triangle is equiangular.
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References

Adapted from CC BY-SA 3.0 Sources:

1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014

Adapted from (Public Domain)

1. Casey, John: "The First Six Books of the Elements of Euclid"