Prove that an equilateral triangle is also equiangular, i.e., all of its angles are equal.

Question

Prove that an equilateral triangle is also equiangular, i.e., all of its angles are equal.

Answer 1

Given: triangle ABC is equilateral. Then that means sides AB = BC = AC, all sides are equal

1) Since AB = BC, then that means angle C = angle A since angles opposite to the equal sides of a triangle are equal.

2) Since BC = AC, then that means angle A = angle B since angles opposite to the equal sides of a triangle are equal.

Therefore by the transitive property, angle A = angle B = angle C

Therefore triangle ABC is equiangular