End Book_1_part_2.
(** The following propositions are valid only in Euclidean geometry, except for Proposition 31, which is valid in neutral geometry. *)
Section Book_1_part_3.
Context `{T2D:Tarski_2D}.
Context `{TE:@Tarski_euclidean Tn TnEQD}.
(** * Proposition 29 A straight line falling on parallel straight lines makes the alternate angles equal to one another, the exterior angle equal to the interior and opposite angle, and the interior angles on the same side equal to two right angles. *)
(** # <div style="width:748px;height:397px;display:block" id="applet_container29"></div> # **)

(* Specifications: *)
Lemma prop_29_1 : forall A D G H, TS G H A D -> Par G A H D -> CongA A G H D H G.
Lemma prop_29_2 : forall B D E G H, Out E G H -> OS E G B D -> Par G B H D ->
CongA B G E D H E.
Lemma prop_29_3 : forall A C G H P Q R, OS G H A C -> Par A G H C -> SumA A G H G H C P Q R ->
Bet P Q R.