Modeling points lines and planes'

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Points, Lines, Planes
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Points

• Undefined term
• No length, width, or thickness
• Named with a capital letter

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Lines

• Undefined term -- No thickness
• Length that goes on forever in two directions

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Naming Lines
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Intersecting LinesLines that share a point.
Y
n
m
Lines m and n intersect. Point Y is the point of
intersection.
6
Parallel LinesLines in the same plane that do
not intersect planes that do not intersect.
k
j
Lines k and j are parallel. k
j
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Skew Lines Lines that do not lie on the same
plane. (They do not intersect and are not
parallel.)

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Plane
W

• Undefined Term
• No thickness
• Extends indefinitely in all directions

Plane ABC Plane W
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Parallel PlanesPlanes not intersect.
Planes R and S are parallel.
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CollinearPoints that are on the same line.

C
B
A
Points A,B and C are collinear.
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Non-collinearPoints that are not on the same
line.

C
B
A
Points A,B and C are non -collinear.
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Coplanar PointsPoints that lie on the same plane.
S
Q
P
R
Points P,Q, and R are coplanar.
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Non-Coplanar PointsPoints that do not lie on the
same plane.
S
Q
P
R
Points P,Q,R and S are non-coplanar.
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Coplanar Lines Lines that lie on the same plane.
x
y
Lines x, y are coplanar.
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Postulates
Statements that are accepted as true.
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Theorems
Statements that are proven to be true.
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Postulate
If two lines intersect, their intersection is a
point.
n
P
m
Lines m and n intersect at P.
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Postulate
For any two points, there is exactly one line
through the points.
B
A
l
Line l is the only line through A and B
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Postulate
For any three noncollinear points, there is
exactly one plane through the points.
B
Q
C
A
Points A, B, and C lie in Plane Q.
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Postulate
If two lines intersect, then they are coplanar.
m
n
Lines m and n lie in only one plane.
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Postulate
If two planes intersect, their intersection is a
line.
Z
W
k
Planes W and Z intersect in line k.
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Postulate
Every plane contains at least three noncollinear
points.
A

Y
Z
X
Plane A contains points X, Y and Z.
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Postulate
Every line contains at least two points.
B
p
A
Line p contains points A and B.
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Postulate
There is exactly one plane containing a given
line and a point not on the line.
? T
?
?
C
D
Only one plane contains T and CD.
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Postulate
If a line and a plane intersect, their
intersection is a point or a line.
t
w
Y
X
I
Line t intersects Plane x at I. Line w intersects
Plane Y at line w.
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Card 7
If two points lie in a plane, then the line
containing them lies in the plane.
B
?
? S
R
If R and S lie in plane B, then RS lies in plane
B.
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Intersecting PlanesPlanes that share a line.
Z
k
W
Planes W and Z intersect. Line k is the line of
intersection.
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Card 6
Space contains at least four noncoplanar points.
?
C
B
D
?
?
?
A
Points A, B, C, and D are noncoplanar.
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Source
http//www.hbschool.com/glossary/ math/glossary8.h
tml