1.2 Points, Lines, and Planes the 3 undefined terms of Geometry - PowerPoint PPT Presentation

1 / 30
About This Presentation
Title:

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

Description:

Geometry 1.2 Points, Lines, and Planes the 3 undefined terms of Geometry * * * * * * * * * * * * * * * * * * * * * * * * * * * * Point No size, no dimensions, it only ... – PowerPoint PPT presentation

Number of Views:2360
Avg rating:3.0/5.0
Slides: 31
Provided by: robesonK
Category:

less

Transcript and Presenter's Notes

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


1
1.2 Points, Lines, and Planesthe 3 undefined
terms of Geometry
Geometry
2
  • 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.
3
  • 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
4
  • Infinite
  • never ending, ongoing
  • Finite
  • limited number, terminates
  • Collinear points
  • points on the same line
  • Noncollinear points
  • points not on the same line

5
  • 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
6
  • Coplanar points
  • Points that lie in the same plane
  • Noncoplanar points
  • points that do not lie in the same plane

7
  • 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.

8
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.
9
Diagram 1
Rectangular Prism faces are rectangles and
bases are always parallel
10
  • Parallel lines
  • Coplanar lines that never intersect
  • Skew lines
  • Noncoplanar lines that never intersect

11
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

12
  • Space
  • The set of all points
  • Noncoplanar points and space are the same

13
  • Postulate
  • 4 noncoplanar points determine space
  • If you can make skew lines out of 4 pts, then you
    know you are in space.

14
Postulates An infinite number of planes can be
passed through a line. Or a line determines an
infinite number of planes.
15
  • 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

16
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!!!!
17
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
18
Postulate the intersection of 2 planes is a line
Plane SUY n Plane CSY in SY
Diagram 2
19
Explain the relationship between 2 planes.
They intersect in a line or they are parallel.
Diagram 3
20
Diagram 3
Give the intersection of the following
Plane UXV n Plane UXQ Plane UQR n Plane
XWS Plane VWS n Plane XUV
21
Explain the relationship between a line and a
plane.
They intersect in a pt or a line.
Diagram 4
22
  • Distribute Geometry Plane and Simple worksheet
    5
  • Allow students to work together for about 5 to 10
    minutes

23
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.

24
  • 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.

25
  • 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.

26
  • assign pgs. 13-15 ( 1-51 odd), (60-66 all) hw

27
Diagram 1
28
Diagram 2
29
Diagram 3
30
Diagram 4
Write a Comment
User Comments (0)
About PowerShow.com