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 CongruentStrictTrianglesSASC : forall A B C A' B' C' : Point,
Distance C A = Distance C' A'  ->
Distance C B = Distance  C' B'  ->
Angle A C B = Angle A' C' B' ->
~Collinear A B C ->
CongruentStrictTriangles A B C A' B' C'.