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Question -

Angles A, B, C of a triangle ABC are equal to each other. Prove that ∆ABC is equilateral.



Answer -

Given : In ∆ABC, ∠A = ∠B = ∠C
 
To prove : ∆ABC is an equilateral
Proof: In ∆ABC,
∴ ∠B = ∠C (Given)
∴ AC = AB …(i) (Sides opposite to equal angles)
Similarly, ∠C = ∠A
∴ BC =AB …(ii)
From (i) and (ii)
AB = BC = CA
Hence ∆ABC is an equilateral triangle

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