Require Export B10_Longueur_Prop.
Section ANGLE_PROPERTIES.

(* Specifications: *)
Lemma AngleSym : forall A B C : Point,
A <> B ->
A <> C ->
Angle B A C = Angle C A B.
Lemma HalfLineAngleB : forall A B C D : Point,
A <> B ->
A <> C ->
HalfLine A B D ->
Angle B A C = Angle D A C.
Lemma HalfLineAngleC : forall A B C D : Point,
A <> B ->
A <> C ->
HalfLine A C D ->
Angle B A C = Angle B A D.
Lemma HalfLineAngleBC : forall A B C D E : Point,
A <> B ->
A <> C ->
HalfLine A B D ->
HalfLine A C E ->
Angle B A C = Angle D A E.
Lemma BetweenAngleBC : forall A B C D E : Point,
Between A B D ->
Between A C E ->
Angle B A C = Angle D A E.
Lemma BetweenAngleC : forall A B C D : Point,
A <> B ->
Between A C D ->
Angle B A C = Angle B A D.
Lemma BetweenAngleB : forall A B C D : Point,
A <> C ->
Between A B D ->
Angle B A C = Angle D A C.
Lemma SASEqualBD : forall A B C D : Point,
Clockwise A B C ->
Clockwise A D C ->
Distance A B = Distance A D ->
Angle B A C = Angle D A C ->
B = D.
Lemma SASEqualCD : forall A B C D : Point,
Clockwise A B C ->
Clockwise A B D ->
Distance A C = Distance A D ->
Angle B A C = Angle B A D ->
C = D.
Lemma AngleBHalfLine : forall A B C D : Point,
Clockwise A B C ->
Clockwise A D C ->
Angle B A C = Angle D A C ->
HalfLine A B D.
Lemma AngleCHalfLine : forall A B C D : Point,
Clockwise A B C ->
Clockwise A B D ->
Angle B A C = Angle B A D ->
HalfLine A C D.