Given that
A, B, C of a triangle ABC are equal to each other.
We have to prove that,
Δ ABC is equilateral.
We have,
∠A = ∠B = ∠C
Now,
∠A = ∠B
BC = AC (Opposite sides to equal angles are equal)
∠B = ∠C
AC = AB (Opposite sides to equal angles are equal)
From the above, we get
AB = BC = AC
Therefore, ΔABC is an quadrilateral triangle.
Hence, proved