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

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Solution

Given: AB = BC = CA

To Prove: ∠A = ∠B = ∠C

Proof:

In ΔABC:
AB = BC (Given)

∠A = ∠C … (1) (Angles opposite to equal sides are equal)

BC = CA (Given)

∠B = ∠A … (2) (Angles opposite to equal sides are equal)

AC = AB (Given)

∠B = ∠C … (3) (Angles opposite to equal sides are equal)

From (1), (2) and (3), ∠A = ∠B = ∠C i.e., the given triangle is equiangular.

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