Points, Lines,
& Planes
Points
l 
Points do not have actual size.
A
l 
How to Sketch:
Using dots
l 
B
How to label:
Use capital letters
Never name two points with the same letter (in the same sketch).
C
A
Lines
l 
Lines extend indefinitely and have no thickness or width.
l 
How to sketch : using arrows at both ends.
n
l 
How to name: 2 ways
(1) small script letter – line n
(2) any two points on the line -
l 
Never name a line using three points -
A
B
C
Line Segment
l 
Line segments do NOT extend indefinitely and have no thickness or width.
l 
How to sketch : draw a line with endpoints.
l 
How to name:
(1) the two endpoints
As with lines, never name a line segment using three points!
Collinear Points
l 
Collinear points are points that lie on the same line. (The line does not have to
be visible!)
Ex:
Collinear
A
B
Non-Ex:
Non collinear
C
A
C
B
*Any two points are collinear. Why?
Planes
l 
A plane is a flat surface that extends indefinitely in all directions.
l 
How to sketch: Use a parallelogram (four sided figure)
l 
How to name: 2 ways
l 
l 
Capital script letter – Plane M
Any 3 non collinear points in the plane - Plane: ABC/ ACB / BAC / BCA /
CAB / CBA
A
B
M
C
Horizontal Plane
Vertical Plane
Other
Different planes in a figure:
A
D
B
H
Plane EFGH
C
E
F
G
Plane ABCD
Plane BCGF
Plane ADHE
Plane ABFE
Plane CDHG
Etc.
Other planes in the same figure:
Any three non collinear points determine a plane!
A
D
B
H
Plane ACGE
C
E
Plane ACH
F
G
Plane AFGD
Plane AGF
Plane BDG
Etc.
Coplanar Objects
Coplanar objects (points, lines, etc.) are objects that lie on
the same plane. The plane does not have to be visible.
A
D
B
C
E
H
F
G
Are the following points coplanar?
A, B, C ?
A, B, C, F ?
H, G, F, E ?
E, H, C, B ?
A, G, F ?
C, B, F, H ?
Yes
No
Yes
Yes
Yes
No
Intersection of Figures
The intersection of two figures is the set of points that
are common in both figures.
The intersection of two lines is a point.
m
P
Line m and line n intersect at point P.
n
Continued…….
3 Possibilities of Intersection of a Line and a Plane
(1) Line passes through plane – intersection is a point.
(2) Line lies on the plane - intersection is a line.
(3) Line is parallel to the plane - no common points.
Intersection of Two Planes is a
Line.
B
P
A
R
!##"
Plane P and Plane R intersect at the line AB
d
n
a
,
s
e
n
i
L
l
e
l
l
a
r
a
P
,
s
Ray
s
e
n
i
L
Skew
es:
Objectiv s
ay
Define r ame rays
lines
w
e
n
k
ly
s
r
d
e
n
Prop
l lines a
e
l
l
a
r
a
p
Identify
Rays
B
A
  A ray is part of a line that consists of one endpoint
and all points of the line extending in one direction
  Name a ray using the endpoint first and then
another point on the ray
  When naming, make sure the arrow points away
from the endpoint.
AB
NOT BA
B
A
AB
Rays, continued
A
  Are these two rays the same?
No
•  Different endpoints
•  Extend in different directions
B
BA
J
K
L
Opposite Rays
  Are two collinear rays with the same endpoint
  Always form a line
KJ and KL are opposite rays
Parallel Lines
  Lines that
  Never intersect
  Extend in the same directions
  Coplanar
Skew lines
Lines that:
  Never intersect
  Are non-coplanar
  Extend in different directions
Parallel Planes
  Parallel planes are planes that never intersect
  Example: the purple planes in the above illustration
  A line and plane that never intersect are also parallel
Learning Check and Summary
  Which of the following has no endpoints?
  Ray, Line Segment, Line
  Which of the following has two endpoints?
  Ray, Line Segment, Line
  Which of the following has one endpoint and extends in one direction?
  Ray, Line Segment, Line
  Which of the following extend in the same direction?
  Parallel lines, skew lines
  Which of the following extend in different directions?
  Parallel lines, skew lines