Equilateral Triangle is Equiangular

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

Then $\triangle ABC$ is also equiangular.

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

By definition of equilateral triangle, any two of the sides of $\triangle ABC$ 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 every two of 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.