1. No category

Lesson 10.1 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˚
© 2011 Carnegie Learning
A
78°
37°
66˚
C
R
m/B 5 180° 2 (78° 1 37°) 5 65°
Chapter 10 Skills Practice • 725
Lesson 10.1 Skills Practice
3. K
4.
page 2
G
35˚
28˚
M
90˚
L
5. W
32˚
F
E
6.
T
110˚
60˚
60˚
X
35˚
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.
726 • Chapter 10 Skills Practice
54˚
s
R
© 2011 Carnegie Learning
60˚
T
Lesson 10.1 Skills Practice
page 3
Name________________________________________________________ Date__________________________
9.
M
10.
Z
k
l
28˚
L
b
X
a
27˚
K
79˚
12.
C
u
B
50˚
d
c
r
30˚
60˚
Z
A
s
90˚
D
© 2011 Carnegie Learning
e
v
t
64˚
W
y
84˚
X
z
Y
Y
67˚
42˚
118˚
m
11.
x
Chapter 10 Skills Practice • 727
Lesson 10.1 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
728 • Chapter 10 Skills Practice
S
© 2011 Carnegie Learning
D
Lesson 10.1 Skills Practice
page 5
Name________________________________________________________ Date__________________________
Solve for x in each diagram.
19.
G
20.
R
x
x
130°
J
F
H
132˚
99°
140˚
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˚
64˚
K
90˚
T
V
S
© 2011 Carnegie Learning
R
(x + 8)
Chapter 10 Skills Practice • 729
Lesson 10.1 Skills Practice
23.
K
page 6
24.
G
(2x + 4)
M
90˚ F
132˚
J
L
112˚
(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
m/
QRT
m/ RTS
,
.m/RST
m/PQR
m/QRT
m/QSR
730 • Chapter 10 Skills Practice
m/QRS
,
m/
© 2011 Carnegie Learning
S
Lesson 10.1 Skills Practice
page 7
Name________________________________________________________ Date__________________________
27.
T
28.
J
U
29.
F
V
W
m/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
m/LMN
m/KLN m/ABC
m/LNM
m/KLN
,
m/
© 2011 Carnegie Learning
m/BAC
m/BCD
Chapter 10 Skills Practice • 731
© 2011 Carnegie Learning
732 • Chapter 10 Skills Practice
Lesson 10.2 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.
© 2011 Carnegie Learning
6. You are given two sides.
Chapter 10 Skills Practice • 733
Lesson 10.2 Skills Practice
page 2
Construct each triangle using the given sides and/or angles.
7. Construct PQR using the three line segments shown.
Q
P
Q
R
R
P
Q
R
P
8. Construct UVW using the three line segments shown.
W
U
W
V
© 2011 Carnegie Learning
U
V
734 • Chapter 10 Skills Practice
Lesson 10.2 Skills Practice
page 3
Name________________________________________________________ Date__________________________
9. Construct DEF using the three line segments shown.
D
F
D
E
E
F
10. Construct MNP using the three line segments shown.
M
P
N
P
N
© 2011 Carnegie Learning
M
Chapter 10 Skills Practice • 735
Lesson 10.2 Skills Practice
page 4
11. Construct HJK using the three line segments shown.
H
K
J
K
H
J
12. Construct ABC using the two line segments and included angle shown.
A
A
B
C
© 2011 Carnegie Learning
A
736 • Chapter 10 Skills Practice
Lesson 10.2 Skills Practice
page 5
Name________________________________________________________ Date__________________________
13. Construct PQR using the two line segments and included angle shown.
Q
P
P
R
P
14. Construct DEF using the two line segments and included angle shown.
D
E
E
F
E
© 2011 Carnegie Learning
Chapter 10 Skills Practice • 737
Lesson 10.2 Skills Practice
page 6
15. Construct KMN using the two line segments and included angle shown.
K
M
M
N
M
16. Construct WXZ using the two line segments and included angle shown.
W
X
W
Z
© 2011 Carnegie Learning
W
738 • Chapter 10 Skills Practice
Lesson 10.3 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
© 2011 Carnegie Learning
4. corresponding angles
5. included angle
6. included side
Chapter 10 Skills Practice • 739
Lesson 10.3 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
740 • Chapter 10 Skills Practice
© 2011 Carnegie Learning
AB 
​  
​ > ​FE ​ 
, ​BC ​ > ​
  EH ​ 
, ​CD ​ > ​
  HG  
​, ​AD ​ > ​
  FG ​ 
, /A > /F, /B > /E, /C > /H, and /D > /G
Lesson 10.3 Skills Practice
page 3
Name________________________________________________________ Date__________________________
3.
B
C
A
4. A
© 2011 Carnegie Learning
B
W
D
X
Z
Y
D
E
C
F
Chapter 10 Skills Practice • 741
Lesson 10.3 Skills Practice
5.
page 4
M
G
J
K
H
6.
T
Q
N
S
P
R
© 2011 Carnegie Learning
U
742 • Chapter 10 Skills Practice
Lesson 10.3 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
© 2011 Carnegie Learning
f
Chapter 10 Skills Practice • 743
Lesson 10.3 Skills Practice
page 6
9. Three sides are given.
h
g
k
10. Two sides and the included angle are given.
b
© 2011 Carnegie Learning
a
744 • Chapter 10 Skills Practice
Lesson 10.3 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
© 2011 Carnegie Learning
f
Chapter 10 Skills Practice • 745
Lesson 10.3 Skills Practice
page 8
13. Two angles and the included side are given.
© 2011 Carnegie Learning
g
746 • Chapter 10 Skills Practice
Lesson 10.3 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
___
__ ___
___ ___
__
MA ​ > ​
  EF ​ 
, ​MT ​ > ​
  JF ​ 
, /M
​   JE ​ , ​AT ​ > ​
> /J,
© 2011 Carnegie Learning
/A > /E, /T > /F
17. nCAT > nDOG
18. nABC > nKTV
19. nPQR > nXYZ
20. nDEF > nRST
Chapter 10 Skills Practice • 747
© 2011 Carnegie Learning
748 • Chapter 10 Skills Practice
Lesson 10.4 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
© 2011 Carnegie Learning
opposite the shortest side. So, the
angles from least to greatest
are /H, /F, /G.
Chapter 10 Skills Practice • 749
Lesson 10.4 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.
750 • Chapter 10 Skills Practice
8. 8 ft, 9 ft, 11 ft
© 2011 Carnegie Learning
3.
page 2
Lesson 10.4 Skills Practice
page 3
© 2011 Carnegie Learning
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 10 Skills Practice • 751
Lesson 10.4 Skills Practice
page 4
Write an inequality that expresses the possible lengths of the unknown side of the given triangle.
___
​?
17. What could be the length of AB ​
​  
___
18. What could be the length of DE 
​  
​?
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
© 2011 Carnegie Learning
2 m , AB , 18 m
752 • Chapter 10 Skills Practice
Lesson 10.4 Skills Practice
page 5
Name________________________________________________________ Date__________________________
___
19. What could be the length of HI ​
​  ​?
___
20.What could be the length of JL 
​ ​?
 
J
I
20 in.
H
14 in.
12 ft
G
7 ft
L
© 2011 Carnegie Learning
K
Chapter 10 Skills Practice • 753
Lesson 10.4 Skills Practice
____
21. What could be the length of MN ​
​ ​?
 
page 6
___
22.What could be the length of QR 
​ ​?
 
P
M
3 cm
N
11 cm
9 mm
13 mm
O
Q
© 2011 Carnegie Learning
R
754 • Chapter 10 Skills Practice