Section SUPPLEMENTARY_ANGLES.
Definition Supplementary (alpha beta : AS) :=
exists A  : Point,  exists B  : Point,  exists C : Point,  exists D : Point,
A <> C /\ Between B A D /\ Angle B A C = alpha /\ Angle C A D = beta.

Lemma HalfLineBetweenBetween : forall A B C D : Point,
Between A C D ->
HalfLine C A B ->
Between B C D.