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Question
Angles A, B, C of a triangle ABC are equal to each other. Prove that ΔABC is equilateral.
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Solution
Given that angles A,B,C of a triangle ABC equal to each other.
We have to prove that ΔABC is equilateral We have, ∠A = ∠B =∠C
Now,
[Opposite sides to equal angles are equal]
and ∠B = ∠C ⇒ AC = AB
From the above we get
AB= BC =AC
⇒ ΔABC is equilateral
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