Section CONGRUENT_STRICT_TRIANGLES.
Definition CongruentStrictTriangles (A B C A' B' C' : Point) :=
CongruentTriangles A B C A' B' C' /\
~Collinear A B C.

Lemma CongruentStrictTrianglesC : forall A B C A' B' C' : Point,
CongruentStrictTriangles A B C A' B' C' ->
Angle A C B = Angle A' C' B'.