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. *)

(* Specifications: *)
Lemma supplement_AM_CongA : forall A B M C, Midpoint M A B -> AM_CongAL  A M C B M C.
Lemma exists_equilateral_triangle : forall A B,
exists C, Cong A B A C /\ Cong A B B C.
(* (** This is Euclid Book I, Prop 35 *)
Lemma parallelograms_same_base :
forall A B C D E F,
Plg A B C D ->
Plg E B C F ->
Col A E F ->
Col D E F ->
signed_area4 A B C D =F= signed_area4 E B C F.