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Points, Lines, & Planes
Objectives
Identify and correctly label points, lines, line segments, rays,
and planes.
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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.
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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
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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
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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
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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 doesmatter for the name of a
ray.
AAAABBBB
AB or BA
AAAA
BBBB
AB
AB is not the same as BA.
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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 its a little
confusing to read.
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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
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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
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Example Find three different ways you can name the plane
below.
Plane T or any three letters except S
S
F R
D
ET
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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.
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Postulate: Through any two points there is exactly one line.
(Euclids 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.
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Postulate: If two planes intersect, then they intersect in
exactly one line.
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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
