Given that angles A, B, C of a triangle ABC equal to each other.

We have to prove that ΔABC is equilateral

We have, ∠A = ∠B = ∠C

Now,

∠A = ∠B ⇒ BC = AC

[Opposite sides to equal angles are equal]

and ∠B = ∠C ⇒ AC = AB

From the above we get

AB = BC = AC

⇒ ΔABC is equilateral