30 Basic shapes of geometry Ch. 2
2.3.2 Exteriorregions
Definition.If|BACis an angle-support which is not straight andIR(|BAC)is its
interior region, then
{Π\IR(|BAC)}∪[A,B∪[A,C
is calledthe exterior region of|BAC, and denoted byER(|BAC). Thus the interior
and exterior regions have in common only the arms.
2.3.3 Angles
Figure 2.8. A wedge-angle. A reflex-angle.A straight-angle.Definition.Let|BACbe an angle-support which is not straight, with interior re-
gionIR(|BAC)and exterior regionER(|BAC). Then the pair
(
|BAC,IR(|BAC)
)
is called awedge-angle,andthepair
(
|BAC,ER(|BAC)
)
is called areflex-angle.If
|BACis a straight-angle support andH 1 ,H 2 are the closed half-planes with common
edgeAB, then each of the pairs(|BAC,H 1 ),(|BAC,H 2 )is called astraight-angle
In each case the pointAis called thevertexof the angle, the half-lines[A,B and
[A,Care called thearmsof the angle, and|BACis called thesupportof the angle.
We denote a wedge-angle with support|BACby∠BAC. The wedge-angle∠BAB
is said to be anull-angle. A reflex-angle with support|BABis called afull-angle.
2.4 Triangles and convex quadrilaterals
2.4.1 Terminology..............................
COMMENT. The terminology which we have used hitherto is established, apart from
‘angle-support’ and ‘wedge-angle’ which we have coined. Now we are reaching ter-
minology which is of long standing but is used in slightly varying senses.
In Euclidean geometry it is generally accepted that the concept of triangle is as-
sociated with:
(i) a set{A,B,C}of three points which are not collinear;(ii) a union of segments[B,C]∪[C,A]∪[A,B], where the pointsA,B,Care as in (i);(iii) an intersection of half-planesH 1 ∩H 3 ∩H 5 ,whereA,B,Care as in (i),H 1 is
the closed half-plane with edgeBCin whichAlies,H 3 is the closed half-plane