Section T11_2.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.
(** This is exterior angle theorem *)
(** In an isosceles triangle the two base angles are equal. This is Euclid: Book 1, Proposition 5. *)
(** This is Euclid: Book 1, Proposition 18 *)
(** If the base angles are equal, then the triangle is isosceles *)
(** This is Euclid Book I, Proposition 19 *)
(** This is SAS congruence. *)
(** This is ASA congruence. *)
(** This is AAS congruence. *)
(** This is SSS congruence. *)
(** This is SSA congruence with a restriction *)
(** This is SSA congruence with an obtuse angle *)
(** This is SSA congruence with a right angle *)
(** The following lemmas express the triangle inequality only with predicates from Tarski : AC <= AB + BC, and AC = AB + BC <-> Bet A B C *)

Lemma triangle_inequality_2 : forall A B C A' B' C',
Bet A' B' C' -> Cong A B A' B' -> Cong B C B' C' ->
Le A C A' C'.