Pulling a One-Eighty! Vocabularychambleems.dekalb.k12.ga.us/Downloads/G7-SSP-CH10-Triangles.pdf ·...
Transcript of Pulling a One-Eighty! Vocabularychambleems.dekalb.k12.ga.us/Downloads/G7-SSP-CH10-Triangles.pdf ·...
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Pulling a One-Eighty!Triangle Sum, Exterior Angle, and Exterior Angle Inequality Theorems
VocabularyWrite 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 SetDetermine the measure of the unknown angle in each triangle.
1.
A
B
C78° 37°
2. P80˚ 66˚
Q
R
m/B 5 180° 2 (78° 1 37°) 5 65°
Lesson 10.1 Skills Practice
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Lesson 10.1 Skills Practice page 2
3. 35˚
28˚
K
LM
4.
90˚ 32˚
F E
G
5.
60˚
60˚
W
X
Y
6.
110˚
35˚
T
V U
List the side lengths from shortest to longest for each diagram.
7.a
b
c
48°
21°
A
B
C 8.
60˚ 54˚
S
T
r t
s R
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.
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Lesson 10.1 Skills Practice page 3
Name _______________________________________________________Date _________________________
9.
28˚118˚
M
K
L
k
l
m
10.
42˚
84˚
Z
YX
yx
z
11.
64˚
79˚67˚
27˚
X Y
W Ze
dca
b 12.
50˚
30˚
60˚90˚
A
u
v
s
r
D
CB
t
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Lesson 10.1 Skills Practice page 4
Identify the interior angles, the exterior angle, and the remote interior angles of each triangle.
13.
WX
Y
Z
14.
R S
UT
Interior angles: /XYZ, /YZX, /ZXY
Exterior angle: /WXZ
Remote interior angles: /XYZ, /YZX
15.
E
F
G H
16. B
C
A
D
17. L
MKJ
18.
Q
P
SR
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Lesson 10.1 Skills Practice page 5
Name _______________________________________________________Date _________________________
Solve for x in each diagram.
19.
F
Gx
H
J
K
130°
99°
20. V
S
TU
R 140˚
132˚
x
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.
H
I
JK
81˚
x2x
22.
R T V S
U
64˚
90˚ (x + 8)
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Lesson 10.1 Skills Practice page 6
23.
132˚
112˚
(2x + 4)
K
L
J
N
M
24.
90˚
(3x + 2) (2x + 18)
F
G
D E
Compare the angles in each triangle and determine the unknown information.
25.
S
RQ
T 26.
S
Q
R
P
m/ QRT .m/RST m/PQR m/QRS
m/ RTS , m/QRT m/QSR , m/
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Lesson 10.1 Skills Practice page 7
Name _______________________________________________________Date _________________________
27. T
U
VW
28. J
F G H
m/TUV m/UWV m/ m/GHJ
m/WVU m/TUV m/GJH m/FGJ
29. K L M
N
30.
D
C
A B
m/LMN m/KLN m/ABC m/BCD
m/LNM m/KLN m/BAC , m/
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Triangle Construction IConstructing Triangles
Problem SetDetermine 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.
6. You are given two sides.
Lesson 10.2 Skills Practice
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Construct each triangle using the given sides and/or angles.
7. Construct PQR using the three line segments shown.
Q R
P R
P Q
P R
Q
8. Construct UVW using the three line segments shown.
U
U
W
W
V
V
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9. Construct DEF using the three line segments shown.
D F
ED
E F
10. Construct MNP using the three line segments shown.
M P
PN
M N
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Lesson 10.2 Skills Practice page 4
11. Construct HJK using the three line segments shown.
H K
KJ
H J
12. Construct ABC using the two line segments and included angle shown.
A B
A
A
C
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Lesson 10.2 Skills Practice page 5
Name _______________________________________________________Date _________________________
13. Construct PQR using the two line segments and included angle shown.
P
P
P R
Q
14. Construct DEF using the two line segments and included angle shown.
D E
E
E
F
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Lesson 10.2 Skills Practice page 6
15. Construct KMN using the two line segments and included angle shown.
K M
M
M
N
16. Construct WXZ using the two line segments and included angle shown.
W
W
W
Z
X
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Triangle Construction IICongruent Figures and Constructing Congruent Triangles
VocabularyDefine each term in your own words.
1. geometric figures
2. congruent geometric figures
3. corresponding sides
4. corresponding angles
5. included angle
6. included side
Lesson 10.3 Skills Practice
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Lesson 10.3 Skills Practice page 2
Problem SetUse 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
D
B
C
E
H
F
G
The figures are congruent.
___
AB > ___
FE , ___
BC > ___
EH , ___
CD > ____
HG , ___
AD > ___
FG , /A > /F, /B > /E, /C > /H, and /D > /G
2. J K
N
P
S
Q
RM
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Lesson 10.3 Skills Practice page 3
Name _______________________________________________________Date _________________________
3. B C
D Z
W X
YA
4. D E
FB C
A
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Lesson 10.3 Skills Practice page 4
5. M
N
K
G
H
J
6.
Q
R
S
T
U
P
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Lesson 10.3 Skills Practice page 5
Name _______________________________________________________Date _________________________
Construct each triangle using the given sides and/or angles.
7. Three sides are given.
a b
c
c
ab
8. Three sides are given.
f
e
d
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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
a
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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
f
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Lesson 10.3 Skills Practice page 8
13. Two angles and the included side are given.
g
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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.
15. MAT > JEF
___
MA > __
JE , ___
AT > ___
EF , ___
MT > __
JF , /M > /J,
/A > /E, /T > /F
17. CAT > DOG
19. PQR > XYZ
16. LMN > GHJ
18. ABC > KTV
20. DEF > RST
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Pasta Anyone?Triangle Inequality Theorem
VocabularyUse the given figure to complete the statement.
1. According to the Triangle Inequality Theorem, 1 . AC.
A C
B
Problem SetWithout measuring the angles, list the angles of each triangle in order from least to greatest measure.
1.
F
G
H8 in.
9 in.
11 in.
2.
X W
Y
4.7 cm3.6 cm
2.1 cm
The smallest angle of a triangle is
opposite the shortest side. So, the
angles from least to greatest
are /H, /F, /G.
Lesson 10.4 Skills Practice
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Lesson 10.4 Skills Practice page 2
3. Q
RP
8 ft 4 ft
6.43 ft
4. T S
U
9 in
12 in
15 in
5. F
E G6 yd
9.2 yd
4.6 yd
6. K
M
L
4.2 m
5.2 m
5.8 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. 8. 8 ft, 9 ft, 11 ft
Yes. Because 3 1 2.9 5 5.9, and
5.9 is greater than 5.
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Lesson 10.4 Skills Practice page 3
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
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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
10 m
B 8 m C
D
6 cm
F 9 cm E
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
2 m , AB , 18 m
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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 ?
I
20 in.
H 14 in. G
J
12 ft
K 7 ft L