NAME
5-3
DATE
PERIOD
Study Guide and Intervention
Inequalities in One Triangle
Angle Inequalities
Properties of inequalities, including the Transitive, Addition, and
Subtraction 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 = b, or a > b.
The Exterior Angle Inequality Theorem can be used to prove this inequality involving an
exterior angle.
B
Exterior Angle
Inequality Theorem
The measure of an exterior angle of a triangle
is greater than the measure of either of its
corresponding remote interior angles.
1
A
C
D
m∠1 > m∠A,
m∠1 > m∠B
Example
List all angles of EFG with measures that are
less than m∠1.
G
4
1 2
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.
3
E
H
F
Use the Exterior Angle Inequality Theorem to list all of
the angles that satisfy the stated condition.
L
3
1 2
1. measures are less than m∠1 ∠3, ∠4
5
4
J
K
Exercises 1–2
M
Lesson 5-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exercises
2. measures are greater than m∠3 ∠1, ∠5
3. measures are less than m∠1 ∠5, ∠6
U
3 5
4. measures are greater than m∠1 ∠7
7
X
5. measures are less than m∠7 ∠1, ∠3, ∠5, ∠6, ∠TUV
6
1 4
2
T
W
Exercises 3–8
V
6. measures are greater than m∠2 ∠4
7. measures are greater than m∠5 ∠1, ∠7, ∠TUV
S
8
8. measures are less than m∠4 ∠2, ∠3
N
7
Q
9. measures are less than m∠1 ∠4, ∠5, ∠7, ∠NPR
1
R
10. measures are greater than m∠4 ∠1, ∠8, ∠OPN, ∠ROQ
Chapter 5
17
2
3
6
5
4
O
Exercises 9–10
P
Glencoe Geometry
NAME
DATE
5-3
PERIOD
Study Guide and Intervention
(continued)
Inequalities in One Triangle
Angle-Side Relationships When the sides of triangles are
not congruent, there is a relationship between the sides and
angles of the triangles.
A
• 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.
B
C
If AC > AB, then m∠B > m∠C.
If m∠A > m∠C, then BC > AB.
• 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
List the angles in order
from smallest to largest measure.
Example 2
List the sides in order
from shortest to longest.
S
6 cm
C
7 cm
R
35°
T
9 cm
20°
A
−−− −− −−
CB, AB, AC
∠T, ∠R, ∠S
125°
B
Exercises
List the angles and sides in order from smallest to largest.
1.
2.
R
T
35 cm
80°
23.7 cm
R
S
∠T, ∠R, ∠S
−− −− −−
RS, ST, RT
6
14
40°
60°
5.
A
T
5
#
5
11
∠S, ∠U, ∠T,
−− −− −−
UT, ST, SU
R
4
18
12
$
8
8.
C
4.0
6.
P
∠B, ∠C, ∠A,
−− −− −−
AC, BA, CB
7. $
4.3
∠C, ∠B, ∠A
−− −− −−
AB, AC, BC
"
5
B
3.8
∠T, ∠R, ∠S
−− −− −−
RS, ST, RT
4.
4
3.
S
Q
20
∠Q, ∠P, ∠R,
−− −− −−
PR, RQ, QP
9.
:
3
35°
%
120°
25°
&
9
∠E, ∠C, ∠D,
−− −− −−
CD, DE, CE
Chapter 5
56°
58°
∠X, ∠Z, ∠Y,
−− −− −−
YZ, XY, XZ
18
;
4
60°
54°
5
∠T, ∠S, ∠R,
−− −− −−
RS, RT, ST
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
48 cm