1.2 Points, Lines, and Planes the 3 undefined terms of Geometry

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1.2 Points, Lines, and Planesthe 3 undefined
terms of Geometry
Geometry
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• Point
• No size, no dimensions, it only has position
• A true point cannot be seen with the naked eye
• Name a point with a capital letter.
• A

Note the dot is only a representation of a pt.
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• Line
• An infinite number of points that extends in 2
  directions
• Name a line with 2 points(2 capital letters)
• Or with one lower case letter

l
Read Line AB or Line l
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• Infinite
• never ending, ongoing
• Finite
• limited number, terminates
• Collinear points
• points on the same line
• Noncollinear points
• points not on the same line

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• Plane
• A flat surface without thickness that extends
  infinitely in all directions

Name a plane with one capital letter that has no
point or with 3 noncollinear points
E
Plane F, Plane ABC, Plane BAC, Plane DAC or
Plane CBA , etc
D
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• Coplanar points
• Points that lie in the same plane
• Noncoplanar points
• points that do not lie in the same plane

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• Postulate or Axiom
• A statement that we assume is true or that we
  accept as fact
• Theorem
• A statement that must be proven true.
• You use definitions, postulates and other
  theorems to prove theorems true.

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Basic Postulates 2 points determine a line. 2
lines intersect in a point 2 planes intersect in
a line 3 planes intersect in a point or a line If
2 pts lie in a plane, then the plane contains
every pt on the line.
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Diagram 1
Rectangular Prism faces are rectangles and
bases are always parallel
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• Parallel lines
• Coplanar lines that never intersect
• Skew lines
• Noncoplanar lines that never intersect

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4 postulates4 ways to determine a plane

• 3 noncollinear pts determine a plane
• A line and a pt not on the line determine a plane
• 2 ll lines determine a plane
• 2 intersecting lines determine a plane

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• Space
• The set of all points
• Noncoplanar points and space are the same

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• Postulate
• 4 noncoplanar points determine space
• If you can make skew lines out of 4 pts, then you
  know you are in space.

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Postulates An infinite number of planes can be
passed through a line. Or a line determines an
infinite number of planes.
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• Any 2 points are collinear
• Any three points lie in the same plane
• Only 3 noncollinear points determine one plane
• Skew lines always indicate space

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Determine if the following sets of points are
collinear, noncollinear (coplanar), or
noncoplanar
(space).

• A,B,C
• E,F,C,B
• G,D
• E,F,A
• G,C,A,B
• F,C
• D,A,R

R
Give a reason for each answer!!!!
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J

• Determine if the following are collinear,
  coplanar, or noncoplanar.
• E,D 5. A,C
• A,B,F 6. E,F,C,B
• G,C,B,A 7. B,D,E,H
• F,A,H,B 8. G,A

9. A, J, B
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Postulate the intersection of 2 planes is a line
Plane SUY n Plane CSY in SY
Diagram 2
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Explain the relationship between 2 planes.
They intersect in a line or they are parallel.
Diagram 3
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Diagram 3
Give the intersection of the following
Plane UXV n Plane UXQ Plane UQR n Plane
XWS Plane VWS n Plane XUV
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Explain the relationship between a line and a
plane.
They intersect in a pt or a line.
Diagram 4
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• Distribute Geometry Plane and Simple worksheet
  5
• Allow students to work together for about 5 to 10
  minutes

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Hapless HairlineTrue/False

• A plane is determined by 2 intersecting lines.
• If 3 pts are coplanar, they are collinear.
• Any 2 pts are collinear.
• A plane and a line intersect at most in one pt.

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• 3 points are not always coplanar.
• 2 planes intersect in infinitely many pts.
• 2 different planes intersect in a line.
• A line lies in one and only one plane.
• A line and a pt not on the line lie in one and
  only one plane.
• 3 planes can intersect in only one pt.

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• 11. 3 lines can intersect in only one pt.
• 3 lines can intersect in only 2 points.
• The intersection of any 2 half-planes is
  necessarily a half-plane.
• The edge of a half-plane is another half-plane.

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• assign pgs. 13-15 ( 1-51 odd), (60-66 all) hw

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Diagram 1
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Diagram 2
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Diagram 3
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Diagram 4