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