Morley's Theorem

Morley's trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the first Morley triangle or simply the Morley triangle. This theorem is listed in the 100 theorem list. In this theory, we define some basics elements on complex geometry such as axial symmetry, rotations. We also define basic property of congruent triangles in the complex field following the model already presented in the afp. In addition we demonstrate sines law in the complex context. Finally we prove the Morley theorem using Alain Connes's proof.