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 CongruentStrictTrianglesCA : forall A B C A' B' C' : Point,
CongruentStrictTriangles A B C A' B' C' ->
Distance C A = Distance C' A'.