Download Practice 5-3 and 5-5

NAME
DATE
5-3
PERIOD
Practice 5-3 and 5-5
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
m∠1
m∠1
D
m∠A,
m∠B
Use the Exterior Angle Inequality Theorem to list all of the angles
that satisfy the stated condition.
L
3
12
1. measures are less than m∠1
M
2. measures are greater than m∠3
5
4
J
K
U
3 5
6. measures are greater than m∠2
3. measures are less than m∠1
7
4. measures are greater than m∠1
7. measures are greater than m∠5
5. measures are less than m∠7
8. measures are less than m∠4
2
1 4
T
X
6
W
V
S
N
8
7
Q
9. measures are less than m∠1
10. measures are greater than m∠4
1
Angle-Side Relationships When the sides of triangles are
6
3
O
5
4
P
Lesson 5-3
R
2
A
not congruent, there is a relationship between the sides and
angles of the triangles.
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.
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.
Exercises
List the angles and sides in order from smallest to largest.
R
1.
S
2.
48 cm
23.7 cm
T
35 cm
S
Chapter 5
3.
80°
R
60°
B
4.3
3.8
40°
A
T
17
4.0
C
Glencoe Geometry
NAME
DATE
5-3
PERIOD
Practice 5-3 and 5-5
4.
U
14
S
5.
5
5
B
T
11
4
P
D 120°
Q
20
9.
Y
35°
18
12
C
8
7. C
R
6.
A
R
8.
25°
E
X
58°
56°
Z
S
60°
54°
T
A
Triangle Inequality
Theorem
The sum of the lengths of any two sides of a
b
triangle must be greater than the length of the third side.
C
c
B
a
a + b > c
b + c > a
a+c>b
Exercises
Is it possible to form a triangle with the given side lengths? If not,
explain why not.
1. 3, 4, 6
2. 8, 8, 8
3. 4, 8, 16
4. 6, 9, 15
5. 2, 4, 5
Find the range for the measure of the third side of a triangle given the measures
of two sides.
7. 1 cm and 6 cm
8. 12 yd and 18 yd
9. 1.5 ft and 5.5 ft
10. 82 m and 8 m
Determine whether the given coordinates are the vertices of a triangle.
11. X(1,-3), Y(6,1), Z(2,2)
Chapter 5
18
Glencoe Geometry