proposition: Lemma PlgExABC1: forall A B C, A <> C -> Col A B C -> Cong A B B C -> exists D, Plg A B C D.
proof: Proof. intros. unfold Col in H0. assert(Midpoint B A C). apply ColCongMid; trivial. exists B. unfold Plg in *. split. tauto. exists B. split. trivial. Midpoint. Qed.
imports: GeoCoq.Tarski_dev.Annexes.perp_bisect