Question

Prove that equilateral triangle is equiangular.

Answer 1

$AB=AC\Rightarrow \angle C=\angle B$ ......$\left(1\right)$since angles opposite to equal sides are equal.

Also,$AC=BC\Rightarrow \angle B=\angle A$ .....$\left(2\right)$ since angles opposite to equal sides are equal.

From $\left(1\right)$ and $\left(2\right)$ we have

$\angle A=\angle B=\angle C$ ...$\left(3\right)$

In $△ABC$,

$\angle A+\angle B+\angle C={180}^{\circ }$(Angle sum property)

$\Rightarrow \angle A+\angle A+\angle A={180}^{\circ }$

$\Rightarrow \angle A=\frac{{180}^{\circ }}{3}={60}^{\circ }$

$\therefore \angle A=\angle B=\angle C={60}^{\circ }$

Hence Proved.