Require Export D4_CongruenceProp.
Section PARALLELOGRAMM_PROP.

(* Specifications: *)
Lemma ExistsDParallelogramm : forall A B C : Point,
Clockwise A B C ->
{D : Point | Parallelogramm A B C D}.
Lemma ParallelogrammCenterClockwiseABI : forall A B C D I : Point,
forall H : Parallelogramm A B C D,
ParallelogrammCenter A B C D H I ->
Clockwise A B I.
Lemma ParallelogrammCenterClockwiseAID : forall A B C D I : Point,
forall H : Parallelogramm A B C D,
ParallelogrammCenter A B C D H I ->
Clockwise A I D.
Lemma ParallelogrammCenterClockwiseICD : forall A B C D I : Point,
forall H : Parallelogramm A B C D,
ParallelogrammCenter A B C D H I ->
Clockwise I C D.
Lemma ParallelogrammCenterClockwiseIBC : forall A B C D I : Point,
forall H : Parallelogramm A B C D,
ParallelogrammCenter A B C D H I ->
Clockwise I B C.
Lemma ParallelogrammCenterCongruentTriangles : forall A B C D I : Point,
forall H : Parallelogramm A B C D,
ParallelogrammCenter A B C D H I ->
CongruentStrictTriangles A I B C I D.
Lemma ParallelogrammCenterBetweenBID : forall A B C D I : Point,
forall H : Parallelogramm A B C D,
ParallelogrammCenter A B C D H I ->
Between B I D.
Lemma ParallelogrammCenterMidPointBD : forall A B C D I : Point,
forall H : Parallelogramm A B C D,
ParallelogrammCenter A B C D H I ->
Distance I B = Distance I D.
Theorem ParallelHalfLine : forall A B C D E : Point,
forall H : Parallelogramm A B C D,
HalfLine C D E ->
Clockwise A B E.
Theorem HalfLineParallel : forall A B C D E : Point,
forall H : Parallelogramm A B C D,
HalfLine D C E ->
Clockwise A B E.
Theorem ParallelClockwise : forall A B C : Point,
Clockwise A B C ->
exists D : Point, EquiDirected A B C D /\ C <> D.
Lemma ParallelogrammParallelogrammBetween : forall A B C D E : Point,
Parallelogramm A B C D ->
Parallelogramm C A B E ->
Between D C E.
Lemma ParallelogrammClockwiseBCD : forall A B C D : Point,
Parallelogramm A B C D ->
Clockwise B C D.
Lemma ParallelogrammClockwiseBDA : forall A B C D : Point,
Parallelogramm A B C D ->
Clockwise B D A.
Lemma ParallelogrammPermut : forall A B C D : Point,
Parallelogramm A B C D ->
Parallelogramm B C D A.
Lemma ParallelogrammSym : forall A B C D E : Point,
Parallelogramm A B C D ->
Distance D C = Distance C E ->
Between D C E ->
Parallelogramm A B E C.