Section Quadrilateral_inter_dec_1.
Context `{TE:Tarski_euclidean}.

Lemma half_plgs :
forall A B C D P Q M,
Parallelogram_strict A B C D ->
Midpoint P A B ->
Midpoint Q C D ->
Midpoint M A C ->
Par P Q A D /\ Midpoint M P Q /\ Cong A D P Q.