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Geometry Basics
Sections covered:
1.3 Points, Lines, & Planes
1.4 Segments, Rays, Parallel Lines, & Planes
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Space
the set of all points
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Points
location in space with no size, represented by a small dot and a letter
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Line
series of points that extends in two opposite directions without endNamed:
AB
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Collinear Points
points that lie on the same line
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Example 1
Are points E, F, and C collinear?Are points E, F, and D collinear?
D
CE F
P
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Plane
flat surface that has no thicknessThink of a sheet of paper
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Coplanar
points and lines in the same plane
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Example 2
Each surface of a cube represents part of a plane. Name the plane represented by the front of the cube.
E
A B
F
G
CD
H
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Postulates & Axioms
Accepted statements of facts
We will use these in proofs to formulate ideas
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Postulate 1-1
Through any two points there is exactly one line.
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Postulate 1-2
If two lines intersect, then they intersect in exactly one point.
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Postulate 1-3
If two planes intersect, then they intersect in exactly one line.
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Example 3
What is the intersection of plane HGFE and plane BCGF?
E
A B
F
G
CD
H
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Postulate 1-4
Through any three noncollinear points there is exactly one plane.
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Example 4
Shade the plane that contains A, B, and C.
E
A B
F
G
CD
H
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Example 4
Shade the plane that contains E, H, and C.
E
A B
F
G
CD
H
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segment
part of a line consisting of two endpoints and all points between them
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ray
part of a line consisting of one endpoint and all the points of the line on one side of the endpoint
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opposite rays
two collinear rays with the same endpointalways form a line!
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Example 5
Name all of the segments and rays in the figure:
L P Q
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parallel lines
coplanar lines that do not intersect
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skew lines
noncoplanar (not parallel and do not intersect)
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Example 6
Name all segments parallel to DC.
Name all segments skew to DC.
N
J I
H
CD
G
M
A B
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Parallel Planes
planes that do not intersect
a line and a plane that do not intersect are also parallel
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Example 7
Use the diagram to name:two pairs of parallel planes
a line that is parallel to plane GHIJ
A
D
B
CI
H
J
G
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Homework…
p. 19: 2-8 even, 14, 20, 38, 40, 50, 52, 55-60
p. 25: 12-23