Chapter 1: Tools of
Geometry
1- 2 Segments, Rays,
Parallel Lines and Planes
Objectives
 1. To identify segments and rays.
 2. To recognize parallel lines, skew lines,
and parallel planes.
 HW/CW: pgs 25-26 #’s 2 – 24 Even
Postulates
Definition: an assumption that needs no explanation.
Examples:
• Through any two points there is
exactly one line.
• A line contains at least two points.
• Through any three noncollinear points,
•there is exactly one plane.
• A plane contains at least three points.
Postulates
Examples:
• If two planes intersect,
then the intersecting is a line.
• If two points lie in a plane,
then the line containing the two
points lie in the same plane.
Segment
Definition: Part of a line containing two endpoints
and all points between them
How to sketch:
A
B
How to name:
AB or BA
The symbol AB is read as "segment AB".
Ray
Definition: RA: is the part of a line consisting of one
endpoint and all the points on one side of the
endpoint
How to sketch:
A
R
R
A
Y
RA or RY ( not RAY )
How to name: RA ( not AR )
( the symbol RA is read as “ray RA” )
The first point represents the ray’s endpoint and the second
point represents the ray’s direction.
Opposite Rays
AX and AY are opposite rays if
A is between X and Y.
Definition:
( Opposite rays must have the same “endpoint” )
X
A
Y
opposite rays
not opposite rays
D
E
DE and ED are not opposite rays.
Parallel Lines
 Parallel lines are two
lines in a plane that
never meet.
 Arrows are used to
indicate lines are
parallel.
 The symbol used for
parallel lines is ||.
A
C
B
D
Pairs of Lines
A
C
B
D
In the above figure, the arrows show that line AB is parallel to line CD.
With symbols we denote, AB || CD .
Skew Lines and Parallel Planes
 Two lines are skew if they do not intersect
and are not in the same plane (not coplanar).
 All planes are either parallel or intersecting.
Parallel planes are two planes that do not
intersect.
Examples
E
H
G
F
C
D
A
1.
2.
3.
4.
B
Name all segments that are parallel to AD
Name all segments that intersect AD
Name all segments that are skew to AD
Name all planes that are parallel to plane ABC.
Answers
1.
2.
3.
4.
Segments EF, BC, & GH.
Segments DE, AB, AF & CD.
Segments CH, BG, FG, & EH.
Plane FGH.