Prove that an equilateral triangle is equiangular

Given: Equilateral triangle PQR

To Prove: ∠P ≅ ∠Q ≅∠R

Proof: PQ ≅ PR ……….[all sides of an equilateral triangle are congruent.]

∠Q ≅ ∠R [the angles opposite to the two congruent sides of a triangle are congruent (Isosceles Triangle Theorem)]

PQ ≅ QR [since all sides of an equilateral triangle are congruent.]

∠R ≅ ∠P, again, by the Isosceles Triangle Theorem

Now, since ∠Q ≅ ∠R and ∠R ≅ ∠P ,

So, ∠Q ≅ ∠P

Therefore, ∠P ≅ ∠Q.

So, equilateral triangles are equiangular.