1. Segments, Angles, and InequalitiesSegments, Angles, and Inequalities
You will learn to apply inequalities to segment and angle
measures.
1) Inequality
Inequalities

2. Segments, Angles, and InequalitiesSegments, Angles, and Inequalities
The Comparison Property of Numbers is used to compare two line segments of
unequal measures.
The property states that given two unequal numbers a and b, either:
a < b or a > b
The same property is also used to compare angles of unequal measures.
T U
2 cm
V W
4 cm
The length of is less than the length of , or TU < VWTU VW

3. Segments, Angles, and InequalitiesSegments, Angles, and Inequalities
J
133°
K
60°
The measure of ∠ J is greater than the measure of ∠ K.
The statements TU > VW and ∠ J > ∠ K are called __________ because
they contain the symbol < or >.
inequalities
Postulate
7 – 1
Comparison
Property
For any two real numbers, a and b, exactly one of the
following statements is true.
a < b a = b a > b

4. Segments, Angles, and InequalitiesSegments, Angles, and Inequalities
6420-2
S D N
Replace with <, >, or = to make a true statement.
SN DN
6 – (- 1) 6 – 2
7 4>
>
Lesson 2-1
Finding Distance
on a number line.

5. Segments, Angles, and InequalitiesSegments, Angles, and Inequalities
Theorem
7 – 1
If point C is between points A and B, and A, C, and B are
collinear, then ________ and ________.
A C B
AB > AC AB > CB
A similar theorem for comparing angle measures is stated below.
This theorem is based on the Angle Addition Postulate.

6. Segments, Angles, and InequalitiesSegments, Angles, and Inequalities
Theorem
7 – 2
then,EFandEDbetweenisEPIf
andDEPmDEFm ∠>∠ PEFmDEFm ∠>∠
D
P
F
E
A similar theorem for comparing angle measures is stated below.
This theorem is based on the Angle Addition Postulate.

7. Segments, Angles, and InequalitiesSegments, Angles, and Inequalities
108°
149°
45°
40°
18°
A
B
C
D
Replace with <, >, or = to make a true statement.
mBDA mCDA
45° 40° + 45°
<
<
Use theorem 7 – 2 to solve the following problem.
CDAmBDAm
then,DAandDCbetweenisDBSince
∠<∠
Check:
CDABDA ∠<∠ mm
45° 85°

8. Segments, Angles, and InequalitiesSegments, Angles, and Inequalities
Property
Transitive
Property
For any numbers a, b, and c,
1) if a < b and b < c, then a < c.
2) if a > b and b > c, then a > c.
if 5 < 8 and 8 < 9, then 5 < 9.
if 7 > 6 and 6 > 3, then 7 > 3.

9. Segments, Angles, and InequalitiesSegments, Angles, and Inequalities
Property
Addition and
Subtraction
Properties
Multiplication
and Division
Properties
For any numbers a, b, and c,
For any numbers a, b, and c,
1) if a < b, then a + c < b + c
and a – c < b – c.
2) if a > b, then a + c > b + c
and a – c > b – c.
1 < 3
1 + 5 < 3 + 5
6 < 8
c
b
c
a
andbcac
thenb,aand0cIf)
<<
<>1
c
b
c
a
andbcac
thenb,aand0cIf)
>>
>>2 3624
218212
1812
<
⋅<⋅
<
96
2
18
2
12
<
<
<1812

10. Segments, Angles, and InequalitiesSegments, Angles, and Inequalities
Property
Addition and
Subtraction
Properties
Multiplication
and Division
Properties
For any numbers a, b, and c,
For any numbers a, b, and c,
1) if a < b, then a + c < b + c
and a – c < b – c.
2) if a > b, then a + c > b + c
and a – c > b – c.
1 < 3
1 + 5 < 3 + 5
6 < 8
c
b
c
a
andbcac
thenb,aand0cIf)
<<
<>1
c
b
c
a
andbcac
thenb,aand0cIf)
>>
>>2 3624
218212
1812
<
⋅<⋅
<
96
2
18
2
12
<
<
<1812