Angles $A, B, C$ of a triangle $ABC$ are equal to each other. Prove that $\triangle ABC$ is equilateral.
Given:
Angles $A, B, C$ of a triangle $ABC$ are equal to each other.
To do:
We have to prove that $\triangle ABC$ is equilateral.
Solution:
In $\triangle ABC, \angle A = \angle B = \angle C$
$\angle B = \angle C$
This implies,
$AC = AB$.....…(i) (Sides opposite to equal angles are equal)
Similarly,
$\angle C = \angle A$
This implies,
$BC =AB$.........…(ii)
From (i) and (ii), we get,
$AB = BC = CA$
Hence, $\triangle ABC$ is an equilateral triangle.
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