Require Export GeoCoq.Tarski_dev.Annexes.circles.
Require Export GeoCoq.Tarski_dev.Annexes.half_angles.
Require Export GeoCoq.Tarski_dev.Ch12_parallel_inter_dec.
Section Inscribed_angle.
Context `{TE:Tarski_euclidean}.
(** The sum of the angles of a triangle is the flat angle. *)

(* Specifications: *)
Lemma trisuma__bet : forall A B C D E F, TriSumA A B C D E F -> Bet D E F.
Lemma bet__trisuma : forall A B C D E F, Bet D E F -> A <> B -> B <> C -> A <> C -> D <> E -> E <> F ->
TriSumA A B C D E F.
Lemma right_saccheris : forall A B C D, Saccheri A B C D -> Per A B C.
Lemma not_obtuse_saccheris : ~ hypothesis_of_obtuse_saccheri_quadrilaterals.
Lemma suma123231__sams : forall A B C D E F, SumA A B C B C A D E F -> SAMS D E F C A B.
Lemma high_school_exterior_angle_theorem : forall A B C B', A <> B -> B <> C -> A <> C -> A <> B' ->
Bet B A B' -> SumA A B C B C A C A B'.