Equilateral Triangle is Equiangular

Theorem
Let $\triangle ABC$ be an equilateral triangle.

Then $\triangle ABC$ is also equiangular.

Proof
By definition of equilateral triangle, any two of its sides are equal.

, let $AB = AC$.

Then by Isosceles Triangle has Two Equal Angles, $\angle ABC = \angle ACB$.

As the choice of equal sides was arbitrary, it follows that any two internal angles of $\triangle ABC$ are equal.

Hence all $3$ internal angles of $\triangle ABC$ are equal.

Also see

 * Equiangular Triangle is Equilateral, of which this is the converse.