Point, Line, Plane

1
Lesson 1-1

• Point, Line, Plane

2
Points

• Points do not have actual size.
• How to Sketch
• Using dots
• How to label
• Use capital letters
• Never name two points with the same letter
• (in the same sketch).

A
B
A
C
3
Lines

• Lines extend indefinitely and have no thickness
  or width.
• How to sketch using arrows at both ends.
• How to name 2 ways
• (1) small script letter line n
• (2) any two points on the line -
• Never name a line using three points -

n
A
B
C
4
Collinear Points

• Collinear points are points that lie on the same
  line. (The line does not have to be visible.)
• A point lies on the line if the coordinates of
  the point satisfy the equation of the line.
• Ex To find if A (1, 0) is collinear with
• the points on the line y -3x 3.
• Substitute x 1 and y 0 in the equation.
• 0 -3 (1) 3
• 0 -3 3
• 0 0
• The point A satisfies the equation, therefore the
  point is collinear
• with the points on the line.

A
B
C
Collinear
C
A
B
Non collinear
5
Planes

• A plane is a flat surface that extends
  indefinitely in all directions.
• How to sketch Use a parallelogram (four sided
  figure)
• How to name 2 ways
• (1) Capital script letter Plane M
• (2) Any 3 non collinear points in the plane -
  Plane ABC/ ACB / BAC / BCA / CAB / CBA

A
M
B
C
Horizontal Plane
Vertical Plane
Other
6
Different planes in a figure
A
B
Plane ABCD Plane EFGH Plane BCGF Plane
ADHE Plane ABFE Plane CDHG Etc.
C
D
E
F
H
G
7
Other planes in the same figure

• Any three non collinear points determine a plane!

Plane AFGD Plane ACGE Plane ACH Plane AGF Plane
BDG Etc.
8
Coplanar Objects

• Coplanar objects (points, lines, etc.) are
  objects that lie on the same plane. The plane
  does not have to be visible.

Are the following points coplanar?
A, B, C ?
Yes
A, B, C, F ?
No
H, G, F, E ?
Yes
E, H, C, B ?
Yes
A, G, F ?
Yes
C, B, F, H ?
No
9
Intersection of Figures

• The intersection of two figures is the set of
  points that are common in both figures.

The intersection of two lines is a point.
m
Line m and line n intersect at point P.
P
n
Continued.
10
3 Possibilities of Intersection of a Line and a
Plane

• (1) Line passes through plane intersection is a
  point.
• (2) Line lies on the plane - intersection is a
  line.
• (3) Line is parallel to the plane - no common
  points.

11

• Segments
• and Rays

12
Postulates
Definition An assumption that needs no
explanation.
Examples

• Through any two points there is
• exactly one line.

• A line contains at least two points.

• Through any three points, there is
• exactly one plane.

• A plane contains at least three points.

13
Postulates
Examples

• If two planes intersect,
• then the intersecting is a line.

• If two points lie in a plane,
• then the line containing the two
• points lie in the same plane.

14
Ray
Definition
How to sketch
How to name
15
Opposite Rays
Definition
If A is between X and Y, AX and AY are opposite
rays.
( Opposite rays must have the same endpoint )
opposite rays
not opposite rays
16
Intersection of Two Planes is a Line.
B
P
A
R
Plane P and Plane R intersect at the line