Aim: What are the undefined terms?
Do Now:
1) What is a point?
2) What is a line?
3) What is a plane?
The most fundamental concepts in geometry do
not have precise definitions but, we understand
their meanings intuitively. We say these concepts
are undefined.
Geometry Leeson: Undefined Terms, 1
Lines, Line Segments
Point: A point indicates a position or location
in space.
Y
. P . A(2, 6)
X
Points are named using
capital letters and/or
coordinates.
Geometry Leeson: Undefined Terms, 2
Lines, Line Segments
Line: A line is an infinite set of adjacent points.
Ex: Curved line
Ex: Straight line
Naming a Line:
a) Two points on the line: AB, AC , BA, BC , etc...
A B C
b) Single lowercase letter
m
Geometry Leeson: Undefined Terms, 3
Lines, Line Segments
Plane: A plane is a set of points that forms a
completely flat surface.
Naming a Plane:
a) Three points on the plane: B•
Plane ABC C•
A•
b) Single uppercase letter:
Plane R
R
Geometry Leeson: Undefined Terms, 4
Lines, Line Segments
Def: Collinear Points: A collinear set of points is a set
of points all of which lie on the
same straight line.
E
A B C D
•Points A, B, C and D are collinear.
•Points A, E and C are not collinear.
Geometry Leeson: Undefined Terms, 5
Lines, Line Segments
Def: Line Segment: A B
A line segment is the set of two points on a line
called endpoints, and all points on the line
between the endpoints.
Naming a Line Segment:
Use the names of the endpoints.
A B
“Line segment” AB is part of “Line” AB
Geometry Leeson: Undefined Terms, 6
Lines, Line Segments
Measure of The measure of a line segment is
Line Segments: the length of the line segment.
To indicate the “measure” of a line
segment, use the name of the line segment
without the line above the name.
Ex: AB = “measure of line segment” AB
Ex: The perimeter of ABC is 58 cm.
If AB = x - 4, BC = 2x + 8, and CA= x – 2,
what is BC? Ans. BC=36 cm
Geometry Leeson: Undefined Terms, 7
Lines, Line Segments
Def: Congruent Line Segments:
Congruent line segments are
segments that are equal in measure.
Ex: A B If AB CD
C D Then AB = CD
Ex: If AB CD , AB 9 x 7 and
CD 4 x 13, what is CD? AB?
Ans. CD = 29, AB = 29
Geometry Leeson: Undefined Terms, 8
Lines, Line Segments
Def: Midpoint The midpoint of a line segment divides the
line segment into two congruent segments.
M
A B
If M is the midpoint of AB , then:
1) AM MB 2) AM MB
1 1
3) AM AB 4) MB AB
2 2
5) AB 2 AM 6) AB 2 MB
Geometry Leeson: Undefined Terms, 9
Lines, Line Segments
Def: Line Bisector The bisector of a line segment is a line that
intersects the line segment at its midpoint.
Q
PMQ is a bisector of AB
A M B
P
If PMQ bisects AB at M, then:
1) M is midpoint of AB
2) M is midpoint of PQ ? X
If PMQ intersects AB at its midpoint M, then:
PMQ is a bisector of AB
Geometry Leeson: Undefined Terms, 10
Lines, Line Segments
Addition and Subtraction of
Line Segments: If several line segments belong to the
same line, we can write addition and
subtraction expressions using the names
S of these segments.
RS RP __
PS
P
RS RP PS
RP RS -__
PS
RP RS PS
PS RS -__
RP
R PS RS RP
Geometry Leeson: Undefined Terms, 11
Lines, Line Segments
Simple 2-Column Proof B
Given: EPF bisects AB at P P F
E
Prove: AP PB
A
Statement Reason
1) EPF bisects AB at P 1) Given
2) P is the midpt. of AB 2) Definition of Line Bisector
3) AP BP 3) Definition of Midpoint
Geometry Leeson: Undefined Terms, 12
Lines, Line Segments