Question:
Angles ΔA, B, C of a triangle ABC are equal to each other. Prove that ABC is equilateral.
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,
∠A = ∠B
BC = AC [opposite sides to equal angles are equal]
And ∠B = ∠C
AC = AB
From the above we get
AB = BC = AC
ΔABC is equilateral.
