Equilateral Triangle is Equiangular

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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.

Without loss of generality, 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.

$\blacksquare$


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