Geometry with Trigonometry

Sec. 1.5 Revision of geometrical concepts 11

A

B

Figure 1.3. A half-line[A,B.

A

B

C

Opposite half-lines.

4. If the pointsB,Care distinct fromA, then the pair of half-lines
   {[A,B,[A,C}is called anangle-supportand denoted by|BAC;if[A,B and[A,C
   are opposite half-lines, then|BACis called astraightangle-support. In each caseAis
   called itsvertex,[A,Band[A,Citsarms.

A

B

C

Figure 1.4. An angle-support.

A

B

C

A straight angle-support.

5. The set of all the points on, or to one side of, a lineABis called aclosed
   half-plane, withedge AB.

A

B

Figure 1.5. A closed half-plane shaded.

6. If the pointsA,B,Care not collinear, then the set of points which are in both the
   closed half-plane with edgeAB, containingC, and the closed half-plane with edge
   AC, containingB, is called theinterior regionof|BACand denoted byIR(|BAC);
   also(Π\IR(|BAC))∪|BACis called theexterior regionof|BACand denoted by
   ER(|BAC).WhenC∈[A,Bthe interior and exterior regions of|BACare taken to be
   [A,BandΠ, respectively.