Show that every equiangular triangle is equilateral.

Let ABC be a triangle with, ∠A = ∠B = ∠C.

Considering, ∠A = ∠B

We get, BC = AC (Sides opposite to equal angles are equal.)

Considering, ∠B = ∠C

We get, AB = BC (Sides opposite to equal angles are equal.)

∴ AB = BC = AC.

Hence, proved that every equiangular triangle is equilateral.