Geometric
Basics
1
Points
• Points do not have actual size.
• How to Sketch:
Using dots
A
B
A
• How to label:
Use capital letters
Never name two points with the same letter in the same sketch.
2
Lines
• Extend indefinitely and have no thickness or width.
• How to sketch : using arrows at both ends.
n
• How to name: 2 ways
(1) small script letter
A
B
C
line n
(2) any two points on the line
AB , BC, AC , BA, CA, CB
• Never name a line using three points
ABC
3
Collinear Points
• Lie on the same line. (The line does not have to be visible).
A
B
C
Non collinear
C
Collinear
A
B
4
Planes
• 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
5
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.
6
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.
7
Coplanar Objects
Coplanar objects (points, lines, etc.) 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 ?
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
8
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.
9
Congruent Segments

Definition: Segments with equal lengths. (congruent symbol: )
B
A
C
D
Congruent segments can be marked with dashes.
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” )
11
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.
12
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
P
n
Line m and line n intersect at point P.
13
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.
14
Intersection of Two Planes is a Line.
AB
B
P
A
R
Plane P and Plane R intersect at the line
15
Segment Bisectors
Definition: Any segment, line or plane that divides a segment into two
congruent parts is called segment bisector.
A
F
A
B
E
AB bisects DF.
B
D
E
AB bisects DF.
F
A
E
D
D
F
Plane M bisects DF.
B
AB bisects DF.
16
Between
Definition: X is between A and B if AX + XB = AB.
X
A
X
AX + XB = AB
B
A
B
AX + XB > AB
17
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.
A x
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
2x
C
B
12
AC + CB = AB
x + 2x = 12
3x = 12
x = 4
x = 4
AC = 4
CB = 8
You Try It!
Complete Practice Problems
and check your answers with
one another.