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NAME ______________________________________________ DATE
5-2
____________ PERIOD _____
Study Guide and Intervention
Inequalities and Triangles
Angle Inequalities
Properties of inequalities, including the Transitive, Addition,
Subtraction, Multiplication, and Division Properties of Inequality, can be used with
measures of angles and segments. There is also a Comparison Property of Inequality.
For any real numbers a and b, either a , b, a 5 b, or a . b.
The Exterior Angle Theorem can be used to prove this inequality involving an exterior angle.
Exterior Angle
Inequality Theorem
If an angle is an exterior angle of a
triangle, then its measure is greater than
the measure of either of its corresponding
remote interior angles.
B
A
1
C
D
m/1 . m/A, m/1 . m/B
Example
G
4
1 2
3
F
E
H
Exercises
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
List all angles that satisfy the stated condition.
L
3
1. all angles whose measures are less than m/1
1 2
M
2. all angles whose measures are greater than m/3
U
3. all angles whose measures are less than m/1
4. all angles whose measures are greater than m/1
5
4
J
K
Exercises 1–2
3 5
7
X
6
1 4
2
T
W
Exercises 3–8
V
5. all angles whose measures are less than m/7
6. all angles whose measures are greater than m/2
7. all angles whose measures are greater than m/5
S
8. all angles whose measures are less than m/4
8
Q
9. all angles whose measures are less than m/1
Chapter 5
13
6
2
1
R
10. all angles whose measures are greater than m/4
N
7
3
5
4
O
Exercises 9–10
P
Glencoe Geometry
Lesson 5-2
List all angles of nEFG whose measures are
less than m/1.
The measure of an exterior angle is greater than the measure of
either remote interior angle. So m/3 , m/1 and m/4 , m/1.
NAME ______________________________________________ DATE
5-2
Study Guide and Intervention
____________ PERIOD _____
(continued)
Inequalities and Triangles
Angle-Side Relationships
When the sides of triangles are
not congruent, there is a relationship between the sides and
angles of the triangles.
A
B
• If one side of a triangle is longer than another side, then the
angle opposite the longer side has a greater measure than the
angle opposite the shorter side.
• If one angle of a triangle has a greater measure than another
angle, then the side opposite the greater angle is longer than
the side opposite the lesser angle.
Example 1
If AC . AB, then m/B . m/C.
If m/A . m/C, then BC . AB.
Example 2
List the angles in order
from least to greatest measure.
List the sides in order
from shortest to longest.
S
C
6 cm
R
C
358
7 cm
9 cm
T
208
A
1258
B
wB
C
w, w
AB
w, w
AC
w
/T, /R, /S
Exercises
List the angles or sides in order from least to greatest measure.
1.
R
2.
3.
S
808
35 cm
S
R
608
4.3
3.8
23.7 cm
T
B
408
T
A
C
4.0
Determine the relationship between the measures of the
given angles.
22
U
24
4. /R, /RUS
T
35
24
25
S
21.6
R
5. /T, /UST
13 V
6. /UVS, /R
Determine the relationship between the lengths of the
given sides.
C
308
308
7. A
wC
w, w
BC
w
A
8. B
wC
w, w
DB
w
308
908
D
B
9. A
wC
w, w
DB
w
Chapter 5
14
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
48 cm