G1
Point, Line, Plane
Point, Line, Plane
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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.
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Points

Points do not have actual size.

How to Sketch:
Using dots

A
B
C
A
How to label:
Use capital letters
Never name two points with the same letter
(in the same sketch).
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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
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Collinear Points

Collinear points are points that lie on the same line. (The line does
not have to be visible.)
A
B
C
Collinear
C
A
B
Non collinear
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Ray
Definition: RA : Has one end point and in other direction
carries on forever more
A
How to sketch:
R
A
Y
R
How to name:
RA ( not AR )
( the symbol RA is read as “ray RA” )
RA or RY ( not RAY )
Opposite Rays
Definition:
X
Opposite rays are created when three points are collinear
The two rays have the same “endpoint”
and can be viewed as a line.
A
Y
opposite rays
not opposite rays
The end point will be between the two other points and we write
X –A-Y
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.
The Segment Addition Postulate
Postulate: If C is between A and B, then AC + CB = AB.
Example:
A
C
AB = AC + CB
Lesson 1-2: Segments and Rays
B
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
Step 2: Label fig. with
given info.
Step 3: Write an
equation
Step 4: Solve and find all the
answers
12
AC + CB = AB
x + 2x = 12
3x = 12
x = 4
x = 4
AC = 4
CB = 8
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
Other
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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.
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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 ?
Yes
No
Yes
Yes
Yes
No
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Intersection of Figures
The intersection of two figures is the set of points that are
common in both figures.
The intersection of two different lines is a point.
m
Line m and line n intersect at point P.
P
n
Continued…….
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2 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.
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Intersection of Two Different Planes is a
Line.
B
P
A
R
Plane P and Plane R intersect at the line AB
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Homework


p. 5 #1,5, 9,10,17
p. 12 #8,10,12, 29
Lesson 1-1 Point, Line, Plane
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