Question

Prove that an equilateral triangle is equiangular.

Answer 1

Given: ∆ABC is an equilateral triangle.

 To prove: ∆ABC is equiangular

 i.e. ∠A ≅ ∠B ≅ ∠C …(i) 

[Sides of an equilateral triangle] 

In ∆ABC, 

seg AB ≅ seg BC [From (i)] 

∴ ∠C = ∠A (ii)

 [Isosceles triangle theorem] 

In ∆ABC, 

seg BC ≅ seg AC [From (i)] 

∴ ∠A ≅ ∠B (iii) [Isosceles triangle theorem] 

∴ ∠A ≅ ∠B ≅ ∠C [From (ii) and (iii)] 

∴ ∆ABC is equiangular.