intros u v H; try assumption.
apply regulier with (a := cons u v) (c := cons u v); auto.
apply transitive with (plus (cons (opp v) u) (cons u v)); auto.
apply transitive with (cons (opp v) v); auto.
apply transitive with pi; auto.
Qed.
Hint Resolve orthogonal_bissectrice.

Lemma bissectrice_hauteur_isocele :
forall I A B C : PO,
bissectrice I A B C -> orthogonal (vec A I) (vec B C) -> isocele A B C.