Section 12: Points, Lines, and Planes - PowerPoint PPT Presentation

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Section 12: Points, Lines, and Planes

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You can name a plane by using a single capital letter, or by using 3 non-collinear points. ... 4: Through any three non-collinear points there is exactly one ... – PowerPoint PPT presentation

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Title: Section 12: Points, Lines, and Planes


1
  • Section 1-2 Points, Lines, and Planes
  • Point is a location. It has no size. When we
    represent a point we use a small dot and a
    Capital letter.
  • Line is a set of points that extend in two
    opposite directions without end. You can name a
    line in two different ways, with two points or
    using a lower case letter. 
  • Collinear points points that lie on the same
    line.

A
t
B
C
2
n
  • Example
  • a. Are points A, B, and C collinear? If so
    name the line.
  • b. Are points A, E, and C collinear? If so
    name the line.
  • c. Name line t in 3 other ways?

m
C
B
A
E
D
t
Yes, line m
No
3
  • Student example
  • a. Name 3 points that are collinear.
  • b. Name 3 points that are not collinear.
  • c. Why do you think arrow heads are used to
    draw or name lines?

A
B
D
E
C
Points A, E, C or Points D, E, C
Answers may vary
Shows continuance in opposite directions without
end.
4
  • Plane is a flat surface that has no thickness.
    A plane contains many lines and extends without
    end in all directions. You can name a plane by
    using a single capital letter, or by using 3
    non-collinear points.
  • Coplaner Points and lines in the same plane are
    called Coplaner.

P
A
Plane ABC or Plane P
C
B
5
  • Student example
  • a. Name the plane in 3 different ways.
  • b. Can you name the plane, Plane B

A
B
D
C
Answers may vary
No, B represents a point and you would need to
use three points to name the plane.
6
  • A postulate or axiom is an accepted statement of
    fact. Always true.
  • Postulate 1-1 through any 2 points there is
    exactly one line.
  • Postulate 1-2 If two lines intersect, then they
    intersect in exactly one point.
  • Postulate 1-3 If two planes intersect, then they
    intersect in exactly one line.
  • Postulate 1-4 Through any three non-collinear
    points there is exactly one plane.

7
H
G
  • Student example
  • a. What is the intersection of plane EFGH and
    Plane CDHG?
  • b. Name two planes that intersect at AB.

E
F
D
C
A
B
Line HG
Plane ABCD and Plane ABEF
8
  • Class work Page 13-15
  • Questions 1-4, 11, 12, 30, 31
  • Homework Page 13-15
  • Questions 5-9, 13-20, 35-41, 45,
  • 60-65, 70-72, 80
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