# 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)

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)

Since the triangle is equilateral and ABD = ACD, so

ABD = ACD = BAC

Hence the triangle is equiangular

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