Question

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

Answer 1

Given : In $\Delta ABC,\angle A=\angle B=\angle C$

To prove : $\Delta ABC\text{is an equilateral}$

Proof : In $\Delta ABC,$

$\therefore \angle B=\angle C\left(Given\right)$

$\therefore AC=AB\left(i\right)$

$\text{(Sides opposite to equal angles)}$

$Similarly,\angle C=\angle A$

$\therefore BC=AB...\left(ii\right)$

$From\left(i\right)and\left(ii\right)$

AB = BC = CA

Hence $\Delta ABC\text{is an equilateral triangle}$