I have tried to make this demonstration, but I have not come up with a concrete idea. If someone can give me an idea of how to perform this demonstration, I would appreciate it very much.
Study and try to demonstrate the following conjecture, on the contrary if you find that it is false, build a counter example.
Let ABC and DEF be two triangles such that the semi-straight line AT is bisector of the angle BAC and the semi-straight line DK is bisector of the angle EDF; the intersection between the semi-straight lines AT and BC is T, the intersection between the semi-straight lines DK and EF is K. If the angles BAC and EDF are congruent, the segments AT and DK are congruent, the segments BC and EF are congruent, then, the triangles ABC and DEF are congruent.