(** * Proposition 27 If a straight line falling on two straight lines make the alternate angles equal to one another, the straight lines will be parallel to one another. *)
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(* Specifications: *)
Lemma prop_27 : forall A D E F, TS E F A D -> CongA A E F D F E -> Par E A F D.
(** * Proposition 28 If a straight line falling on two straight lines make the exterior angle equal to the interior and opposite angle on the same side, or the interior angles on the same side equal to two right angles, the straight lines will be parallel to one another. *)
(** # <div style="width:748px;height:397px;display:block" id="applet_container28"></div> # **)
Lemma prop_28_1 : forall B D E G H, Out E G H -> OS E G B D -> CongA B G E D H E ->
Par G B H D.
Lemma prop_28_2 : forall A C G H P Q R, OS G H A C -> SumA A G H G H C P Q R -> Bet P Q R ->
Par A G C H.