Suppose a triangle is equilateral. Prove that it is equiangular.

Δ ABC is an equilateral triangle

Let AD be the perpendicular from A on BC

In Δ ABD and Δ ACD

AB = AC (ΔABC is equilateral)

∠ADB = ∠ADC (AD is a perpendicular)

AD = AD (Common side)

So Δ ABD and Δ ACD are congruent to each other by S.A.S. axiom of congruency

∠ABD = ∠ACD (Corresponding Parts of Congruent Triangles)

∠BAD = ∠CAD (Corresponding Parts of Congruent Triangles)

Since the triangle is equilateral and ∠ABD = ∠ACD, so

∠ABD = ∠ACD = ∠BAC

Hence the triangle is equiangular