How angles opposite to the sides of an equiangular triangle influence the similarity of these sides?

Question

I hope that the sides opposite to the angles of an equiangular triangle are called homologous sides because these sides are similar.

I would like to know why angles opposite to the sides of an equiangular triangle influence the similarity of these sides. This question developed from this discussion.

Answer 1

If the triangle is equiangular, it is automatically equilateral. Just stop and think; you have three equal angles and you try to form a triangle with them. You cannot stretch nor elongate the sides,otherwise the angles are going to change ; it is perfectly symmetrical.

Answer 2

If two triangles have the same corner angles, then those are moved, rotated and/or scaled copies.

--- rk