This document defines and provides examples of key geometric concepts including points, lines, line segments, rays, planes, and their relationships. It defines points as having no dimensions, lines as straight paths extending indefinitely, line segments as parts of lines between two endpoints, and rays as parts of lines extending from an endpoint in one direction. Planes are defined as flat surfaces extending indefinitely. Examples are provided to demonstrate collinear points that lie on the same line, coplanar points that lie in the same plane, and basic postulates such as two points defining a single unique line. Key terms are summarized in a table for easy reference.

1. Points, Lines, & Planes
Objectives
• Identify and correctly label points, lines, line segments,
rays, and planes.

2. point A location in space, represented by a
capital letter. (No dimension)
• A Point A
Notation: A point is always labeled with a
capital printed letter. It has no size —
one point is not bigger than another.

3. line A straight path that has no thickness and
extends forever in both directions.
(1 dimension)
Example:
AB or line
Notation: A line is labeled either by two
points or a single lowercase letter. The
order of the two letters does not
matter. (AB is the same as BA.)
•
•
AAAA
BBBB

4. collinear
noncollinear
Points that lie on the same line.
Example:
Points A, B, and C are collinear.
Points that do not lie on the same line.
Points A, B, and D are noncollinear
Note: Two points are always collinear.
•
•
A
C
B
•
D
•

5. Examples
1. Are points G, H, and J collinear or
noncollinear?
2. Are points F, H, and K collinear or
noncollinear?
3. Are points J and K collinear or
noncollinear?
F
•
H
•
G
•
J
•
K
•
collinear
noncollinear
collinear

6. line segment
ray
Part of a line consisting of two points,
called endpointsendpointsendpointsendpoints, and all points between
them.
Part of a line that starts at an endpoint
and extends forever in one direction.
Notation: The order of the letters does
matter for the name of a ray.
AAAA
BBBB
AB or BA
AAAA
BBBB
•
AB
AB is not the same as BA.

7. opposite rays Two rays that have a common endpoint and
form a line.
Q
• R
• S
•
RS and RQ are opposite rays
Note: You could also write RQ as QR.
although it’s a little confusing to read.

8. plane A flat surface that has no thickness and
extends forever. (2 dimensions)
Plane ABC or plane R
Notation: A plane is named either by a
script capital letter or three
noncollinear points.
A
•
B
•
C
•
R

9. coplanar
noncoplanar
Points that lie in the same plane.
Example:
Points A, B, C, and D are coplanar.
Points that do not lie in the same plane.
Points A, B, C, and E are noncoplanar.
Note: Three noncollinear points are always
coplanar.
A
•
B
•
C
•
R
E
•
D
•

10. Example Find three different ways you can name the
plane below.
Plane T or any three letters except S
S
F R
D
E
T
•
• •
•
•

11. undefined term
postulate
A basic figure that cannot be defined in
terms of other figures
Points, lines, and planes are undefined
terms — all other geometric figures are
defined in terms of them. Our “definitions”
are just descriptions of their attributes.
A statement that is accepted as true
without proof. Also called an axiom.

12. Postulate: Through any two points there is
exactly one line. (Euclid’s first postulate)
Postulate: Through any three noncollinear
points there is exactly one plane
containing them.
Postulate: If two lines intersect, then they
intersect in exactly one point.
•

13. Postulate: If two planes intersect, then
they intersect in exactly one line.

14. Examples:
1. The intersection of
planes H and E is
____ or ____.
2. The intersection of m
and n is ____.
3. Line k intersects E at
____.
4. R, X, and S are
__________.
n
XXXX
YYYY
collinearcollinearcollinearcollinear
k
E
H
m
n
R
X
S
Y
•
•
RSRSRSRS