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 SupplementBC : forall A B C D A' B' C' D' : Point,
A <> C ->
A' <> C' ->
B <> C ->
Between B A D ->
Between B' A' D' ->
Angle B A C = Angle B' A' C' ->
Angle C A D = Angle C' A' D'.