Question

In the $∆\mathrm{ABC},\mathrm{AB}\cong \mathrm{BC}\cong \mathrm{AC}$.

What kind of triangle is this?

Answer 1

Given: In $∆\mathrm{ABC},$ $\mathrm{AB}\cong \mathrm{BC}\cong \mathrm{AC}$

$\bullet$$\mathrm{AB}\cong \mathrm{BC}$

⇒ $\mathrm{AB}$ is congruent to $\mathrm{BC}$

⇒ $\mathrm{AB}=\mathrm{BC}$

$\bullet$$\mathrm{BC}\cong \mathrm{AC}$

⇒ $\mathrm{BC}$ is congruent to $\mathrm{AC}$

⇒ $\mathrm{BC}=\mathrm{AC}$

$\bullet$$\mathrm{AB}\cong \mathrm{AC}$

⇒ $\mathrm{AB}$ is congruent to $\mathrm{AC}$

⇒ $\mathrm{AB}=\mathrm{AC}$

Thus, in $∆\mathrm{ABC},$

Hence, $\mathrm{AB}=\mathrm{BC}=\mathrm{CA}$

Thus, given $∆\mathrm{ABC}$is an equilateral triangle.