Question

Prove that the three angles of an equilateral triangle are equal.

Answer 1

Given:-

let ABC is an equilateral triangle

$\therefore AB=BC=AC$

(all sides of an equilateral triangle are equal)

To prove:

$\angle A=\angle B=\angle C$

Proof:

$AB=AC$

$⟹\angle B=\angle C$ .......(1) $[\because$ angles opposite to equal sides are equal $]$

$BC=AC$

$⟹\angle A=\angle B$ .........(2) $[\because$ angles opposite to equal sides are equal $]$

From (1) and (2)

$\angle A=\angle B=\angle C$

Hence proved.