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