3∠ ⇒ equilat — Three equal angles ⇒ equilateral · Principia

Dependencies: Isoceles converse: equal base angles ⇒ equal sides (a triangle with two equal angles has two equal legs).

Statement

Let the three interior angles of $\triangle ABC$ be equal to one another:

\angle A = \angle B = \angle C.

Then the three sides are equal too: $AB = BC = CA$ . That is, "equal angles" pulls "equal sides" all the way down along the same correspondence.

$Equivalence between equal angles and equilateral: \angle A = \angle B = \angle C \Longleftrightarrow AB = BC = CA — angles and sides are pinned together inside an equilateral triangle$

Three equal angles ⇒ equilateral

Statement

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