Definition weak_parallelogram (A B C D : Point) : Prop :=
  A<>C /\ B<>D /\
  exists O, mid_point O A C /\ mid_point O B D.

(* Specifications: *)
Lemma parallelogram_weak_parallelogram : forall A B C D, parallelogram A B C D -> weak_parallelogram A B C D.
Theorem weak_parallelogram_parallelogram : forall A B C D, ~ Col A B C -> weak_parallelogram A B C D -> parallelogram A B C D.
Theorem l2_11a_strong : forall A B C D P Q : Point, weak_parallelogram A B C D -> S A P Q + S C P Q = S B P Q + S D P Q.
Theorem l2_11a : forall A B C D P Q : Point, parallelogram A B C D -> S A P Q + S C P Q = S B P Q + S D P Q.