Identify and correctly label points, lines, line segments, rays, and planes

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

2. pointpointpointpoint – 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.another.

3. linelinelineline – a straight path that has no thickness and extends
forever in both directions. (1 dimension)
Example:
•
•
A
B m
AB or BA or line m
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.)

4. collinearcollinearcollinearcollinear – points that lie on the same line.
Example:
Points A, B, and C are collinear.
•
•
A
C
B
•
D
•
noncollinearnoncollinearnoncollinearnoncollinear – points that do not lie on the same line.
Points A, B, and D are noncollinear.
Two points are always collinear.
(note)

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

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

7. line segment – part of a line consisting of two points, called
endpointsendpointsendpointsendpoints, and all points between them.
ray – part of a line that starts at an endpoint and extends
forever in one direction.
A
B
orAB BA
Notation: The order of the letters does matter for the
name of a ray.
A
B
•
AB
AB is not the same as BA.

8. opposite rays – two rays that have a common endpoint and
form a line.
Q
• R
• S
•
and are opposite raysRS RQ
You could also write RQ as QR (note the arrow
direction), although it’s a little confusing to read.

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

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

11. Example Find three different ways you can name the
plane below.
S
F R
D
E

 


E
T 

12. Example Find three different ways you can name the
plane below.
S
F R
D
E

 


PlanePlanePlanePlane TTTT or any three letters exceptor any three letters exceptor any three letters exceptor any three letters except SSSS
E
T 

13. undefined termundefined termundefined termundefined term – 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.
postulatepostulatepostulatepostulate – a statement that is accepted as true withoutpostulatepostulatepostulatepostulate – a statement that is accepted as true without
proof. Also called an axiom.

14. 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.exactly one point.


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

16. 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 ____.
k
E
H
m
n
R
X
S
Y


4. R, X, and S are __________.
n

17. 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 ____.
n
X
Y
k
E
H
m
n
R
X
S
Y


RS
4. R, X, and S are __________.collinear
n