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Chapter 10 Skills Practice

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Lesson 10.1тАГ Skills Practice
Name________________________________________________________ Date__________________________
Pulling a One-Eighty!
Triangle Sum, Exterior Angle, and Exterior Angle Inequality Theorems
Vocabulary
Write the term that best completes each statement.
1. The
states that the measure of an exterior angle of a
triangle is greater than the measure of either of the remote interior angles of the triangle.
2. The
states that the sum of the measures of the interior
angles of a triangle is 180┬░.
3. The
states that the measure of an exterior angle of a
triangle is equal to the sum of the measures of the remote interior angles of the triangle.
4. The
are the two angles that are
non-adjacent to the specified exterior angle.
Problem Set
Determine the measure of the unknown angle in each triangle.
1. B
2. P
Q
80╦Ъ
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A
78┬░
37┬░
66╦Ъ
C
R
m/B 5 180┬░ 2 (78┬░ 1 37┬░) 5 65┬░
Chapter 10тАВ тАВ тАВ Skills PracticeтАВ тАВ тАВ тАвтАВ тАВ тАВ 725
Lesson 10.1тАГ Skills Practice
3. K
4.
page 2
G
35╦Ъ
28╦Ъ
M
90╦Ъ
L
5. W
32╦Ъ
F
E
6.
T
110╦Ъ
60╦Ъ
60╦Ъ
X
35╦Ъ
V
U
Y
List the side lengths from shortest to longest for each diagram.
7.
B
C
a
48┬░
8.
S
b
c
21┬░
t
r
A
m/C 5 180┬░ 2 (48┬░ 1 21┬░) 5 111┬░
The shortest side of a triangle
is opposite the smallest angle. So, the side lengths from shortest
to longest are a, b, c.
726тАВ тАВ тАВ тАвтАВ тАВ тАВ Chapter 10тАВ тАВ тАВ Skills Practice
54╦Ъ
s
R
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60╦Ъ
T
Lesson 10.1тАГ Skills Practice
page 3
Name________________________________________________________ Date__________________________
9.
M
10.
Z
k
l
28╦Ъ
L
b
X
a
27╦Ъ
K
79╦Ъ
12.
C
u
B
50╦Ъ
d
c
r
30╦Ъ
60╦Ъ
Z
A
s
90╦Ъ
D
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e
v
t
64╦Ъ
W
y
84╦Ъ
X
z
Y
Y
67╦Ъ
42╦Ъ
118╦Ъ
m
11.
x
Chapter 10тАВ тАВ тАВ Skills PracticeтАВ тАВ тАВ тАвтАВ тАВ тАВ 727
Lesson 10.1тАГ Skills Practice
page 4
Identify the interior angles, the exterior angle, and the remote interior angles of each triangle.
13.
14.
Y
W
U
T
X
Z
R
S
Interior angles: /XYZ, /YZX, /ZXY
Exterior angle: /WXZ
Remote interior angles: /XYZ, /YZX
15.
F
E
G
16.
B
C
H
A
17.
L
18.
P
Q
J
K
M
R
728тАВ тАВ тАВ тАвтАВ тАВ тАВ Chapter 10тАВ тАВ тАВ Skills Practice
S
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D
Lesson 10.1тАГ Skills Practice
page 5
Name________________________________________________________ Date__________________________
Solve for x in each diagram.
19.
G
20.
R
x
x
130┬░
J
F
H
132╦Ъ
99┬░
140╦Ъ
S
V
T
U
K
m/GFH 5 180┬░ 2 130┬░ 5 50┬░
m/GHK 5 m/GFH 1 m/FGH
99┬░ 5 50┬░ 1 x
49┬░ 5 x
21.
I
H
x
22.
U
2x
J 81╦Ъ
64╦Ъ
K
90╦Ъ
T
V
S
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R
(x + 8)
Chapter 10тАВ тАВ тАВ Skills PracticeтАВ тАВ тАВ тАвтАВ тАВ тАВ 729
Lesson 10.1тАГ Skills Practice
23.
K
page 6
24.
G
(2x + 4)
M
90╦Ъ F
132╦Ъ
J
L
112╦Ъ
(3x + 2)
D
(2x + 18)
E
N
Compare the angles in each triangle and determine the unknown information.
25.
T
Q
R
26.
R
P
Q
S
тАЙm/
QRT
m/ RTS
,
.m/RST
m/PQR
m/QRT
m/QSR
730тАВ тАВ тАВ тАвтАВ тАВ тАВ Chapter 10тАВ тАВ тАВ Skills Practice
m/QRS
,
m/
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S
Lesson 10.1тАГ Skills Practice
page 7
Name________________________________________________________ Date__________________________
27.
T
28.
J
U
29.
F
V
W
тАЙm/TUV
m/UWV
m/WVU
m/TUV
K
m/
H
m/GHJ
m/GJH
M
L
G
m/FGJ
30. A
B
C
N
D
тАЙm/LMN
m/KLNтАЙm/ABC
m/LNM
m/KLN
,
m/
┬й 2011 Carnegie Learning
m/BAC
m/BCD
Chapter 10тАВ тАВ тАВ Skills PracticeтАВ тАВ тАВ тАвтАВ тАВ тАВ 731
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732тАВ тАВ тАВ тАвтАВ тАВ тАВ Chapter 10тАВ тАВ тАВ Skills Practice
Lesson 10.2тАГ Skills Practice
Name________________________________________________________ Date__________________________
Triangle Construction I
Constructing Triangles
Problem Set
Determine whether each combination of given sides and/or angles determines a unique triangle.
1. You are given three angles.
No.
2. You are given three sides.
3. You are given two sides and the included angle.
4. You are given two angles and a side not specified.
5. You are given two angles.
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6. You are given two sides.
Chapter 10тАВ тАВ тАВ Skills PracticeтАВ тАВ тАВ тАвтАВ тАВ тАВ 733
Lesson 10.2тАГ Skills Practice
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Construct each triangle using the given sides and/or angles.
7. Construct юБоPQR using the three line segments shown.
Q
P
Q
R
R
P
Q
R
P
8. Construct юБоUVW using the three line segments shown.
W
U
W
V
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U
V
734тАВ тАВ тАВ тАвтАВ тАВ тАВ Chapter 10тАВ тАВ тАВ Skills Practice
Lesson 10.2тАГ Skills Practice
page 3
Name________________________________________________________ Date__________________________
9. Construct юБоDEF using the three line segments shown.
D
F
D
E
E
F
10. Construct юБоMNP using the three line segments shown.
M
P
N
P
N
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M
Chapter 10тАВ тАВ тАВ Skills PracticeтАВ тАВ тАВ тАвтАВ тАВ тАВ 735
Lesson 10.2тАГ Skills Practice
page 4
11. Construct юБоHJK using the three line segments shown.
H
K
J
K
H
J
12. Construct юБоABC using the two line segments and included angle shown.
A
A
B
C
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A
736тАВ тАВ тАВ тАвтАВ тАВ тАВ Chapter 10тАВ тАВ тАВ Skills Practice
Lesson 10.2тАГ Skills Practice
page 5
Name________________________________________________________ Date__________________________
13. Construct юБоPQR using the two line segments and included angle shown.
Q
P
P
R
P
14. Construct юБоDEF using the two line segments and included angle shown.
D
E
E
F
E
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Chapter 10тАВ тАВ тАВ Skills PracticeтАВ тАВ тАВ тАвтАВ тАВ тАВ 737
Lesson 10.2тАГ Skills Practice
page 6
15. Construct юБоKMN using the two line segments and included angle shown.
K
M
M
N
M
16. Construct юБоWXZ using the two line segments and included angle shown.
W
X
W
Z
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W
738тАВ тАВ тАВ тАвтАВ тАВ тАВ Chapter 10тАВ тАВ тАВ Skills Practice
Lesson 10.3тАГ Skills Practice
Name________________________________________________________ Date__________________________
Triangle Construction II
Congruent Figures and Constructing Congruent Triangles
Vocabulary
Define each term in your own words.
1. geometric figures
2. congruent geometric figures
3. corresponding sides
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4. corresponding angles
5. included angle
6. included side
Chapter 10тАВ тАВ тАВ Skills PracticeтАВ тАВ тАВ тАвтАВ тАВ тАВ 739
Lesson 10.3тАГ Skills Practice
page 2
Problem Set
Use measuring tools to determine whether the given figures are congruent. If the figures are congruent,
then identify and list the corresponding sides and angles. If the figures are not congruent, explain why
they are not.
1.
A
B
D
C
E
F
H
G
The figures are congruent.
___
___ ___
___ ___
____ ___
___
2. J
K
P
Q
N
M
S
R
740тАВ тАВ тАВ тАвтАВ тАВ тАВ Chapter 10тАВ тАВ тАВ Skills Practice
┬й 2011 Carnegie Learning
ABтАп
тАЛ тАп
тАЛ > тАЛFEтАптАЛтАп
, тАЛBCтАптАЛ > тАЛ
тАп EHтАптАЛтАп
, тАЛCDтАптАЛ > тАЛ
тАп HGтАптАп
тАЛ, тАЛADтАптАЛ > тАЛ
тАп FGтАптАЛтАп
, /A > /F, /B > /E, /C > /H, and /D > /G
Lesson 10.3тАГ Skills Practice
page 3
Name________________________________________________________ Date__________________________
3.
B
C
A
4. A
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B
W
D
X
Z
Y
D
E
C
F
Chapter 10тАВ тАВ тАВ Skills PracticeтАВ тАВ тАВ тАвтАВ тАВ тАВ 741
Lesson 10.3тАГ Skills Practice
5.
page 4
M
G
J
K
H
6.
T
Q
N
S
P
R
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U
742тАВ тАВ тАВ тАвтАВ тАВ тАВ Chapter 10тАВ тАВ тАВ Skills Practice
Lesson 10.3тАГ Skills Practice
page 5
Name________________________________________________________ Date__________________________
Construct each triangle using the given sides and/or angles.
7. Three sides are given.
b
a
c
b
a
c
8. Three sides are given.
d
e
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f
Chapter 10тАВ тАВ тАВ Skills PracticeтАВ тАВ тАВ тАвтАВ тАВ тАВ 743
Lesson 10.3тАГ Skills Practice
page 6
9. Three sides are given.
h
g
k
10. Two sides and the included angle are given.
b
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a
744тАВ тАВ тАВ тАвтАВ тАВ тАВ Chapter 10тАВ тАВ тАВ Skills Practice
Lesson 10.3тАГ Skills Practice
page 7
Name________________________________________________________ Date__________________________
11. Two sides and the included angle are given.
c
d
12. Two sides and the included angle are given.
e
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f
Chapter 10тАВ тАВ тАВ Skills PracticeтАВ тАВ тАВ тАвтАВ тАВ тАВ 745
Lesson 10.3тАГ Skills Practice
page 8
13. Two angles and the included side are given.
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g
746тАВ тАВ тАВ тАвтАВ тАВ тАВ Chapter 10тАВ тАВ тАВ Skills Practice
Lesson 10.3тАГ Skills Practice
page 9
Name________________________________________________________ Date__________________________
14. Two angles and the included side are given.
h
Use the congruence symbol to show the corresponding sides and angles that are congruent based on
each congruence statement.
16. nLMN > nGHJ
15. nMAT > nJEF
___
__ ___
___ ___
__
MAтАптАЛ > тАЛ
тАп EFтАптАЛтАп
, тАЛMTтАптАЛ > тАЛ
тАп JFтАптАЛтАп
, /M
тАЛ тАп JEтАптАЛтАп, тАЛATтАптАЛ > тАЛ
> /J,
┬й 2011 Carnegie Learning
/A > /E, /T > /F
17. nCAT > nDOG
18. nABC > nKTV
19. nPQR > nXYZ
20. nDEF > nRST
Chapter 10тАВ тАВ тАВ Skills PracticeтАВ тАВ тАВ тАвтАВ тАВ тАВ 747
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748тАВ тАВ тАВ тАвтАВ тАВ тАВ Chapter 10тАВ тАВ тАВ Skills Practice
Lesson 10.4тАГ Skills Practice
Name________________________________________________________ Date__________________________
Pasta Anyone?
Triangle Inequality Theorem
Vocabulary
Use the given figure to complete the statement.
1. According to the Triangle Inequality Theorem,
. AC.
1
B
A
C
Problem Set
Without measuring the angles, list the angles of each triangle in order from least to greatest measure.
1.
G
2.
Y
9 in.
8 in.
F
4.7 cm
H
3.6 cm
11 in.
X
2.1 cm
W
The smallest angle of a triangle is
┬й 2011 Carnegie Learning
opposite the shortest side. So, the
angles from least to greatest
are /H, /F, /G.
Chapter 10тАВ тАВ тАВ Skills PracticeтАВ тАВ тАВ тАвтАВ тАВ тАВ 749
Lesson 10.4тАГ Skills Practice
8 ft
P
5.
Q
4.
4 ft
6.43 ft
T
9 in
15 in
6.
K
9.2 yd
4.2 m
5.8 m
4.6 yd
E
6 yd
S
U
R
F
12 in
L
G
M
5.2 m
Determine whether it is possible to form a triangle using segments with the given measurements.
Explain your reasoning.
7. 3 in., 2.9 in., 5 in.
Yes. Because 3 1 2.9 5 5.9, and
5.9 is greater than 5.
750тАВ тАВ тАВ тАвтАВ тАВ тАВ Chapter 10тАВ тАВ тАВ Skills Practice
8. 8 ft, 9 ft, 11 ft
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3.
page 2
Lesson 10.4тАГ Skills Practice
page 3
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Name________________________________________________________ Date__________________________
9. 4 m, 5.1 m, 12.5 m
10. 7.4 cm, 8.1 cm, 9.8 cm
11. 10 yd, 5 yd, 21 yd
12. 13.8 km, 6.3 km, 7.5 km
13. 112 mm, 300 mm, 190 mm
14. 20.2 in., 11 in., 8.2 in.
15. 30 cm, 12 cm, 17 cm
16. 8 ft, 8 ft, 8 ft
Chapter 10тАВ тАВ тАВ Skills PracticeтАВ тАВ тАВ тАвтАВ тАВ тАВ 751
Lesson 10.4тАГ Skills Practice
page 4
Write an inequality that expresses the possible lengths of the unknown side of the given triangle.
___
тАЛ?
17. What could be the length of ABтАптАЛ
тАЛ тАп
___
18. What could be the length of DEтАп
тАЛ тАп
тАЛ?
A
D
6 cm
10 m
F
B
8m
9 cm
E
C
AB , AC 1 BC
AB , 10 m 1 8 m
AB , 18 m
AC , AB 1 BC
AC 2 BC , AB
10 m 2 8 m , AB
2 m , AB
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2 m , AB , 18 m
752тАВ тАВ тАВ тАвтАВ тАВ тАВ Chapter 10тАВ тАВ тАВ Skills Practice
Lesson 10.4тАГ Skills Practice
page 5
Name________________________________________________________ Date__________________________
___
19. What could be the length of HIтАптАЛ
тАЛ тАптАЛ?
___
20.What could be the length of JLтАп
тАЛ тАЛ?
тАп
J
I
20 in.
H
14 in.
12 ft
G
7 ft
L
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K
Chapter 10тАВ тАВ тАВ Skills PracticeтАВ тАВ тАВ тАвтАВ тАВ тАВ 753
Lesson 10.4тАГ Skills Practice
____
21. What could be the length of MNтАптАЛ
тАЛ тАЛ?
тАп
page 6
___
22.What could be the length of QRтАп
тАЛ тАЛ?
тАп
P
M
3 cm
N
11 cm
9 mm
13 mm
O
Q
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R
754тАВ тАВ тАВ тАвтАВ тАВ тАВ Chapter 10тАВ тАВ тАВ Skills Practice
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