How you can prove that the angles of two triangles are equal?

If the angles of two triangles are equal the triangles are similar.

AAA If you have three angles on both triangles these must be equal for the triangles to be similar.

SAS If you have an angle between two sides and the length of the sides and the angle are the same on both triangles, then the triangles are similar.

And SSS If you know the three sides