Prove that an equilateral triangle is equiangular.

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Solution

Consider an equilateral triangle ABC.

In △ABC, AB = BC
∴ ∠C = ∠A ...(1) (Angles opposite to equal sides)
In △ABC, AB = CA
∴ ∠C = ∠B ...(2) (Angles opposite to equal sides)
From (1) and (2), we get
∠A = ∠B = ∠C

Hence, an equilateral triangle is equiangular.

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Prove that an equilateral triangle is equiangular.

Consider an equilateral triangle ABC. In △ABC, AB = BC ∴ ∠C = ∠A ...(1) (Angles opposite to equal sides) In △ABC, AB = CA ∴ ∠C = ∠B ...(2) (Angles opposite to equal sides) From (1) and (2), we get ∠A = ∠B = ∠C Hence, an equilateral triangle is equiangular.

Consider an equilateral triangle ABC.

In △ABC, AB = BC
∴ ∠C = ∠A ...(1) (Angles opposite to equal sides)
In △ABC, AB = CA
∴ ∠C = ∠B ...(2) (Angles opposite to equal sides)
From (1) and (2), we get
∠A = ∠B = ∠C

Hence, an equilateral triangle is equiangular.