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Question
Prove that an equilateral triangle is equiangular.
Sum
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Solution
Consider an equilateral triangle ABC.
In △ABC,
AB ≅ BC
∴ ∠ACB = ∠BAC ...(1)...(Angles opposite to equal sides)
In △ABC,
AB ≅ CA
∴ ∠ACB = ∠ABC ...(2)...(Angles opposite to equal sides)
From (1) and (2), we get
∠BAC ≅ ∠ABC ≅ ∠ACB
Hence, an equilateral triangle is equiangular.
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