Angles A, B, C of a triangle ABC are equal to each other. Prove that Δ ABC is equilateral.
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Given : Angles A, B, C of a triangle ABC are equal to each other.
To prove : Δ ABC is equilateral.
We have,
∠A = ∠B = ∠C
Now,
∠A = ∠B
BC = AC ………….(1)
[sides Opposite to equal angles are equal]
∠B = ∠C
AC = AB ……………(2)
[sides Opposite to equal angles are equal]
From the eq 1 and 2 , we get
AB = BC = AC
Therefore, Δ ABC is equilateral.
Hence, proved
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