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7/30/2019 Obj. 4 Points, Lines, And Planes
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Obj. 4 Points, Lines, & PlanesObjectives
Identify and correctly label points, lines, line segments,rays, and planes.
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postulate
point
A statement that is accepted as true
without proof. Also called an axiom.
A location in space, represented by a
capital letter.
A Point A
Notation: A point is always labeled with acapital 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.
Example:
AB or line
Notation: A line is labeled either by twopoints or a single lowercase letter. Theorder 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 ornoncollinear?
2. Are points F, H, and K collinear ornoncollinear?
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 betweenthem.
Part of a line that starts at an endpointand 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.
QQQQ RRRR
SSSS
RS and RQ are opposite rays
Note: You could also write RQ as QR.
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plane A flat surface that has no thickness and
extends forever.
Plane ABC or planeR
Notation: A plane is named either by ascript 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 alwayscoplanar.
A
B
C
R
E
D
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Example Find three different ways you can name the
plane below.
Plane Tor any three letters except S
S
F R
D
ET
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Post. 1-1-1: Through any two points there is
exactly one line.
Post. 1-1-2: Through any three noncollinearpoints there is exactly one planecontaining them.
Post. 1-1-4: If two lines intersect, then they
intersect in exactly one point.
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Post. 1-1-5: If two planes intersect, then
they intersect in exactly one line.
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Examples:
1. The intersection ofplanes Hand E is____ or ____.
2. The intersection ofmand n is ____.
3. Line kintersects Eat ____.
4. R, X, and S are
__________.
n
XXXX
YYYY
collinearcollinearcollinearcollinear
k
E
H
m
n
R
X
S
Y
RSRSRSRS