Geometry with Trigonometry

Sec. 1.5 Revision of geometrical concepts 13

in triangles, we could take|BAC=[A,B∪[A,C. However whenAis betweenBand
C, this would result in a straight-angle being a line, and it would not have a unique
vertex. In the early part of our course, we can confine our attention to wedge and
straight angles.

A B

C

Figure 1.8. Supports bearing two angles each.

A B

C

8. IfAis betweenBandCandD∈BC, the wedge-angles∠BAD,∠CADare
   calledsupplementary.IfA,B,Care not collinear, andAis betweenBandB 1 ,andAis
   betweenCandC 1 , then the wedge-angles∠BAC,∠B 1 AC 1 are calledopposite angles
   at a vertex.

C A B

D

Figure 1.9. Supplementary angles.

 A

B

C

B 1

C 1

Opposite angles at a vertex.

9. IfA,B,Care non-collinear points and[A,D is in the interior region of|BAC,
   then[A,Dissaidtobebetween[A,Band[A,C.

A

B

C

D

Figure 1.10.[A,Dbetween[A,Band[A,C.

10. IfA,B,Care non-collinear points, letH 1 be the closed half-plane with edge
    BC, containingA,H 3 be the closed half-plane with edgeCA, containingB,H 5 be
    the closed half-plane with edgeAB, containingC. Then the intersectionH 1 ∩H 3 ∩