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.

(* 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.
Lemma triangles_same_base : forall A B C D, Par A D B C -> signed_area A B C =F= signed_area D B C.