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5.2 Inequalities and Triangles
Geometry
Read page 280 to complete the properties below:
Properties of Inequalities for Real Numbers:
Comparison Property:
Transitive Property:
Addition and Subtraction Properties:
Multiplication and Division Properties:
2
External Angle Inequality Theorem:
If an angle is an exterior angle of a triangle, then its measure is
1
Example 1: Determine which angle has the greatest measure.
3
4
2
1
5
4
3
Example 2: Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition.
A. measures less than m8
1
2
B. measures greater than m2
7
3
6
4
C. measures less than m3
5
8
Example 3: Use the Exterior Angle Inequality to list all of the angles that satisfy the stated condition.
A. measures less than m14
17
16
3
5
4
B. measures greater than m5
11
10
9
2
1
12
8
7
14
15
6
P
Theorem 5.9: If one side of a triangle is longer than another side, then…
R
Q
C
15
Example 4: Determine the relationship between the measures of the given angles.
D
A. ADB, DBA
16
12
8
B. CBD, CDB
A
10
Example 5: Determine the relationship between the measures of the given angles.
A. RSU , SUR
R
B. TSV , STV
5.2
S
3.6
4.8
4.4
V
5.1
U
A
E
110
Example 6: Determine the relationship between BC and EC.
B. What is the longest side in the figure?
30 
40 
B
T
6.6
5.3
C. RSV , RUV
B
55 
100
50 
D
C
Example 7: Triangle ABC has vertices A(2,1), B(3, 4), and C (0, 2) . List the angles in order from least to the
greatest measure.
Example 8: Find the value of n. List the sides of PQR in order from shortest to longest if
mP  6n  4, mQ  7n  12, and mR  6n  7.