Sign of an isosceles triangle

Theorem

If the two angles in the triangle are equal, then it is isosceles.



Evidence.

Let triangle ABC be such that ∠ A = ∠ B. Let us prove that it is isosceles.



The triangle ACB is equal to the triangle BCA, according to the second sign of equality of triangles, since AB = BA, ∠ A = ∠ B, ∠ B = ∠ A. Therefore, AC = BC. We obtain that the triangle ABC is isosceles. The theorem is proved.