Point, Line, Plane
Point, Line, Plane
1
Geometry Terms
•Undefined terms: words that do not have a formal
definition but there is agreement about what they mean.
•Defined terms: Terms that can be described using known
words
•Postulate or Axiom: Rule that is accepted without proof.
•Theorem: Rule that can be proved.
Point, Line, Plane
2
Points

Points do not have actual size.

How to Sketch:
A
Using dots

B
C
A
How to label:
Use capital letters
Never name two points with the same letter
(in the same sketch).
Point, Line, Plane
3
Lines


Lines extend indefinitely and have no thickness or width.
How to sketch : using arrows at both ends.
n
A
B


C
How to name: 2 ways
(1) small script letter – line n
(2) any two points on the line - AB , BC, AC , BA, CA, CB
Never name a line using three points - ABC
Point, Line, Plane
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
A
B
C
the points on the line y = -3x + 3.
Substitute x = 1 and y = 0 in the equation.
Collinear
0 = -3 (1) + 3
C
0 = -3 + 3
A
0=0
B
The point A satisfies the equation, therefore the point is collinear
Non collinear
with the points on the line.
Lesson 1-1 Point, Line, Plane
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
B
M
C
Horizontal Plane
Vertical Plane
Lesson 1-1 Point, Line, Plane
Other
6
Different planes in a figure:
A
D
B
C
E
H
Plane EFGH
F
G
Plane ABCD
Plane BCGF
Plane ADHE
Plane ABFE
Plane CDHG
Etc.
Lesson 1-1 Point, Line, Plane
7
Other planes in the same figure:
Any three non collinear points determine a plane!
A
D
B
Plane AFGD
Plane ACGE
C
Plane ACH
E
H
F
G
Plane AGF
Plane BDG
Etc.
Lesson 1-1 Point, Line, Plane
8
Coplanar Objects
Coplanar objects (points, lines, etc.) are objects that lie on
the same plane. The plane does not have to be visible.
A
D
B
C
E
H
F
G
Are the following points coplanar?
A, B, C ?
A, B, C, F ?
H, G, F, E ?
E, H, C, B ?
A, G, F ?
C, B, F, H ?
Lesson 1-1 Point, Line, Plane
Yes
No
Yes
Yes
Yes
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
Lesson 1-1 Point, Line, Plane
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.
Lesson 1-1 Point, Line, Plane
11
Intersection of Two Planes is a Line.
B
P
A
R
Plane P and Plane R intersect at the line AB
Lesson 1-1 Point, Line, Plane
12
Ray
Definition: RA : RA and all points Y such that
A is between R and Y.
A
How to sketch:
R
A
Y
R
How to name:
RA ( not AR )
RA or RY ( not RAY )
( the symbol RA is read as “ray RA” )
Lesson 1-2: Segments and Rays
Opposite Rays
Definition: If A is between X and Y, AX and AY are opposite rays.
( Opposite rays must have the same “endpoint” )
X
A
Y
opposite rays
not opposite rays
D
E
DE and ED are not opposite rays.
Lesson 1-2: Segments and Rays
Segment
Definition: Part of a line that consists of two points called the
endpoints and all points between them.
How to sketch:
How to name:
A
B
AB or BA
The symbol AB is read as "segment AB".
AB (without a symbol) means the length of
the segment or the distance between points
A and B.
Lesson 1-2: Segments and Rays
The Segment Addition Postulate
Postulate: If C is between A and B, then AC + CB = AB.
Example: If AC = x , CB = 2x and AB = 12, then, find x, AC
and CB.
B
2x
A x C
Step 1: Draw a figure
12
Step 2: Label fig. with
given info.
Step 3: Write an
equation
Step 4: Solve and find all the
answers
AC + CB = AB
x + 2x = 12
3x = 12
x = 4
Lesson 1-2: Segments and Rays
x = 4
AC = 4
CB = 8
Homework
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
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Pg. 5 # 1
Pg 6 # 17, 18, 20
Pg 12 # 8, 10, 12
Pg 13 #21 to 26, 29
Lesson 1-2: Formulas