Proof with Geometry.
intros.
apply weak_parallelogram_weak_3_parallelogram.
apply parallelogram_weak_parallelogram.
assumption.
Qed.

Lemma parallel_side_eq_weak_weak_para :   forall P Q C D,
parallel P Q C D ->
(P = D <-> Q = C) ->
P ** Q = C ** D ->
weak_2_parallelogram P Q D C.