Proof with Geometry.
intros.
unfold weak_3_parallelogram in *.
DecompExAnd H X.
exists X...
Qed.

(* Specifications: *)
Lemma weak_3_parallelogram_weak_3_parallelogram_2 :
forall A B C D,
weak_3_parallelogram A B C D ->
weak_3_parallelogram C D A B.
Lemma weak_3_parallelogram_weak_3_parallelogram_3 :
forall A B C D,
weak_3_parallelogram A B C D ->
weak_3_parallelogram D A B C.
Lemma weak_3_parallelogram_weak_3_parallelogram_4 :
forall A B C D,
weak_3_parallelogram A B C D ->
weak_3_parallelogram D C B A.