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

1 / 30
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:
Tags:
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