Question

Prove that an equilateral triangle is equiangular.

Answer 1

Consider an equilateral triangle ABC.

In △ABC,

AB ≅ BC

∴ ∠ACB = ∠BAC         ...(1)...(Angles opposite to equal sides)

In △ABC,

AB ≅ CA

∴ ∠ACB = ∠ABC          ...(2)...(Angles opposite to equal sides)

From (1) and (2), we get

 ∠BAC ≅ ∠ABC ≅ ∠ACB

Hence, an equilateral triangle is equiangular.