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

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