252 List of axioms
(iii) if∠BAC is a wedge-angle and the point D=A lies in the interior region
IR(|BAC),then|∠BAD|◦+|∠DAC|◦=|∠BAC|◦,while if|BACis a straight angle-support and D∈AB, then|∠BAD|◦+|∠DAC|◦=180;(iv) if B=A, ifH 1 is a closed half-plane with edge AB, and if the half-lines[A,C
and[A,DinH 1 are such that|∠BAC|◦=|∠BAD|◦,then[A,D=[A,C;(v)if B=A, ifH 1 is a closed half-plane with edge AB, and if 0 <k< 180 ,then
there is a half-line[A,CinH 1 such that|∠BAC|◦=k.AXIOM A 6 .If triangles T and T′, with vertices{A,B,C}and{A′,B′,C′}, respec-
tively, are such that
|C,A|=|C′,A′|,|A,B|=|A′,B′|,|∠BAC|◦=|∠B′A′C′|◦,then T(A,B,C)→≡(A′,B′C′)T′.
AXIOM A 7 .Given any line l∈Λand any point P∈l, there is at most one line m
such that P∈m and l‖m.