Section CONGRUENT_TRIANGLES.
Definition CongruentTriangles (A B C A' B' C' : Point) :=
Distance A B = Distance A' B' /\
Distance B C = Distance  B' C' /\
Distance C A = Distance C' A'.

Lemma CongruentTrianglesCA : forall A B C A' B' C' : Point,
CongruentTriangles A B C A' B' C' ->
Distance C A = Distance C' A'.