Definition AM_CongAL A B C D E F := Py A B C * twice_signed_area D E F =F= Py D E F * twice_signed_area A B C.
(** This shows that we have a notion of congruence of line angles, every angle is congruent to its supplement. *)

Lemma exists_equilateral_triangle : forall A B,
exists C, Cong A B A C /\ Cong A B B C.