Prove that two equilateral triangles are similar.

The first sign of the similarity of triangles sounds like this: if two angles of one triangle are respectively equal to two angles of another triangle, then the triangles are similar.
By definition, an equilateral triangle is a regular polygon with three sides. All sides of a regular triangle are equal to each other, all angles are also equal and amount to 60 °.
Therefore, according to the first sign of similarity of triangles, two equilateral triangles are similar. Since the two corresponding angles of one triangle are equal to two of the other triangle and are equal to 60 °.