Require Export D5_ParalleleConst.
Section SUM_ANGLES_PROPERTIES.

(* Specifications: *)
Lemma SumAnglesRec : forall A B C D E : Point,
Clockwise A B C ->
Clockwise A C D ->
Between B A E ->
Angle B A C = Angle A C D ->
Angle D A E = Angle A D C.
Lemma SumAnglesCorollary : forall A B C D E A' B' C' : Point,
Clockwise A' B' C' ->
Clockwise A B C ->
Clockwise A C D ->
Angle B A C = Angle A' B' C' ->
Angle C A D = Angle B' A' C' ->
Between B A E ->
Angle D A E = Angle A' C' B'.
Lemma TwoEmbeddedTriangles : forall A B C D E : Point,
Clockwise A B C ->
Between A D B ->
Between A E C ->
Angle A D E = Angle A B C ->
Angle A E D = Angle A C B.
Lemma TwoEmbeddedSymTriangles : forall A B C D E : Point,
Clockwise A B C ->
Between A D B ->
Between A E C ->
Angle A E D = Angle A C B ->
Angle A D E = Angle A B C.
Lemma ExternParallelogramm  : forall A B C D E : Point,
Parallelogramm A B C D ->
Between D C E ->
Angle A B C = Angle B C E.
Lemma ExternOppParallelogramm  : forall A B C D E : Point,
Parallelogramm A B C D ->
Between B C E ->
Angle A B C = Angle D C E.
Lemma ParallelogrammExtern  : forall A B C D E : Point,
Parallelogramm A B C D ->
Clockwise C B E ->
Angle A B C = Angle B C E ->
Between D C E.