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Chapter I
Preliminaries from Geometry
This chapter contains definitions, axioms, and theorems from geometry which are needed for what follows. They serve to insure that the reader and the authors have a common terminology for the material which is prerequisite to the study of trigonometry, so they are, for the most part, presented as facts without formalism or proof.
1. Rays and Segments
A point P on a (straight) line
divides 
into two half-lines, each of which is a ray with P as its
only endpoint. A ray
extends infinitely in one direction. Let P and Q be distinct points and
be the unique line passing through them. Then the
ray PQ designates the ray with P as endpoint
which passes through Q. Also, the segment PQ consists of
P and Q and all the
points between these endpoints on the line
By specifying P as the initial point and Q as the final point,
the segment PQ
becomes the "directed segment"
Directed segments 
and 
have the same magnitude if the lengths of the segments are equal, as in Figure 1.
Figure 1
If 
and
are on parallel lines,
(or are on the same line), they may have the same direction, as in Figure 2a, or they
may have opposite directions, as in Figure 2b.
Figure 2a Figure 2b
If directed segments
and
have the same magnitude and direction as in Figure 3, this will
be denoted by the notation
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