split.
apply symmetry_preseves_bet2;
assumption.
intro.
eapply (symmetry_preseves_bet1 A B);
assumption.
Qed.

Lemma par_cong_mid : forall A B A' B', Par A B A' B' -> Cong A B A' B' -> exists M,  Midpoint M A A' /\ Midpoint M B B' \/ Midpoint M A B' /\ Midpoint M B A'.
intros.