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Lesson 11.1 • Similar Polygons
Name
Period
Date
All measurements are in centimeters.
1. HAPIE NWYRS
AP _____
2. QUAD SIML
6 A
H
5
EI _____
I
E
24
N
YR _____
S
Y
R
21
S
8
MI _____
W
18
SN _____
120°
SL _____
P
4
I 85°
mD _____
L
A
D
M
25
13
mU _____
75°
mA _____
Q
20
U
In Exercises 3–6, decide whether or not the figures are similar. Explain why
or why not.
4. ABC and ADE
3. ABCD and EFGH
H
A 120° B
3
60°
D
9
120°
15
E
A
8
O
4
3
B
4
7
G
14
12
C
8
6. ABCD and AEFG
5 K
10
3
F
5. JKON and JKLM
N
E
4
60°
E
J
6
D
B
C
3
2
2
60°
5
A
G
120°
F
4
3
20
M
L
D
7. Draw the dilation of ABCD by a scale
factor of 12. What is the ratio of the
perimeter of the dilated quadrilateral
to the perimeter of the original
quadrilateral?
7
C
8. Draw the dilation of DEF by a scale factor
of 2. What is the ratio of the area of the
dilated triangle to the area of the original
triangle?
y
y
B (4, 6)
5
5
D (1, 2)
C (3, 3)
A (0, 2)
F (2, 1)
D (4, 1)
5
72
CHAPTER 11
E (4, 1)
5
x
x
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Lesson 11.2 • Similar Triangles
Name
Period
Date
All measurements are in centimeters.
M
1. TAR MAC
C
3
MC _____
A
2
R
2. XYZ QRS
T
7
3. ABC EDC
4. TRS TQP
Q _____
A _____
TS _____
QR _____
CD _____
QP _____
QS _____
AB _____
Y
6
20
X
Z
28
R
A
R
E
1
20 _4
B
12
T
8
16
17
S
30
C
P
Q
1
22 _2
9
8
S
Q
D
For Exercises 5 and 6, refer to the figure at right.
16
5. Explain why CAT and DAG are similar.
D
6. CA _____
C
48
A
12 G
T
In Exercises 7–9, identify similar triangles and explain why they are similar.
7.
8.
B
9.
Q
M
N
P
R
C
A
E
D
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T
L
O
K
S
CHAPTER 11
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Lesson 11.3 • Indirect Measurement with Similar Triangles
Name
Period
Date
1. At a certain time of day, a 6 ft man casts a 4 ft shadow. At the same
time of day, how tall is a tree that casts an 18 ft shadow?
2. Driving through the mountains, Dale has to go up and over a high
mountain pass. The road has a constant incline for 734 miles to the
top of the pass. Dale notices from a road sign that in the first mile
he climbs 840 feet. How many feet does he climb in all?
3. Sunrise Road is 42 miles long between the edge of Moon Lake
and Lake Road and 15 miles long between Lake Road and
Sunset Road. Lake Road is 29 miles long. Find the length of
Moon Lake.
Sunrise Road
Moon
Lake
Lake
Road
Sunset Road
4. Marta is standing 4 ft behind a fence 6 ft 6 in. tall. When
she looks over the fence, she can just see the top edge of a
building. She knows that the building is 32 ft 6 in. behind
the fence. Her eyes are 5 ft from the ground. How tall is
the building? Give your answer to the nearest half foot.
Fence
Building
5 ft
6 ft 6 in.
4 ft
32 ft 6 in.
5. You need to add 5 supports under the ramp, in addition to
the 3.6 m one, so that they are all equally spaced. How long
should each support be? (One is drawn in for you.)
Ramp
Support
3.6 m
9.0 m
74
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Lesson 11.4 • Corresponding Parts of Similar Triangles
Name
Period
Date
All measurements are in centimeters.
1. ABC PRQ. M and N
2. The triangles are similar.
are midpoints. Find h and j.
Find the length of each side of the
smaller triangle to the nearest 0.01.
R
1.5
1.2
h
P
Q
N
B
12
3.2
j
2.4
A
8
C
M
3
10
3. ABC WXY
4. Find x and y.
WX _____
AD _____
DB _____
YZ _____
10
x
XZ _____
y
8
5
C
14
Y
28
D
16
A
B
24
W
5. Find a, b, and c.
12
Z
X
6. Find CB, CD, and AD.
A
3
c
25
7
6
C
b
D
B
4
a
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Lesson 11.5 • Proportions with Area
Name
Period
Date
All measurements are in centimeters unless otherwise indicated.
4
Area of circle O
1. ABC DEF. Area of ABC 15 cm2.
2. .
9
Area of circle P
Area of DEF _____
a _____
A
D
6 cm
3 cm
5 cm
F
a
E
C
P
O
B
Area of square SQUA
Area of square LRGE
Area of circle P
Area of circle O
3. _____ 4. _____
G
E
12␲
A
S
5. RECT ANGL
Area of RECT
_____
Area of ANGL
C
T
L
10
P
2␲
3
Q
L
U
5
R
O
4
A
R
G
N
E
6. The ratio of the corresponding midsegments of two similar trapezoids
is 4:5. What is the ratio of their areas?
7. The ratio of the areas of two similar pentagons is 4:9. What is the ratio
of their corresponding sides?
8. If ABCDE FGHIJ, AC 6 cm, FH 10 cm, and area of
ABCDE 320 cm2, then area of FGHIJ _____.
9. Stefan is helping his mother retile the kitchen floor. The tiles are
4-by-4-inch squares. The kitchen is square, and the area of the floor is
144 square feet. Assuming the tiles fit snugly (don’t worry about
grout), how many tiles will be needed to cover the floor?
76
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Lesson 11.6 • Proportions with Volume
Name
Period
Date
All measurements are in centimeters unless otherwise indicated.
In Exercises 1 and 2, decide whether or not the two solids are similar.
1.
2.
4
20
3
16
5
12
8
8
2
32
6
1.5
5
3. The triangular prisms are similar and the ratio of a to b is 2.
Volume of large prism 250
cm3
b
a
Volume of smaller prism _____
4. The right cylinders are similar and r 10 cm.
R
Volume of large cylinder 64 cm
Volume of small cylinder 8 cm
R _______
r
5. The corresponding heights of two similar cylinders is 2:5. What is the
ratio of their volumes?
6. A rectangular prism aquarium holds 64 gallons of water. A similarly
shaped aquarium holds 8 gallons of water. If a 1.5 ft2 cover fits on the
smaller tank, what is the area of a cover that will fit on the larger tank?
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Lesson 11.7 • Proportional Segments Between Parallel Lines
Name
Period
Date
All measurements are in centimeters.
BC
?
2. Is XY
1. x _____
A
MK
?
3. Is XY
M
A
8
6
3
2
9
X
4.5
3
C
B
T
P
40
Y
X
ᐉ
x
4. NE _____
N
12.5
60
6. a _____
PQ _____
b _____
RI _____
M
8
12
A
15
5
Q
b
5
4.5
3
E
I
R
A
8. x _____
9. p _____
EB _____
y _____
q _____
R
E
S
15
10
B
30
5
T
y
2
12
9
12
CHAPTER 11
q
3
4
x
4
78
T
a
7. RS _____
15
O
n
10
P
48
Y
5. PR _____
T
3
P
M
K
30
p
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3. V 890.1 cm3; S 486.9 cm2
6. CA 64 cm
4. V 34.1
7. ABC EDC. Possible explanation: A E
and B D by AIA, so by the AA Similarity
Conjecture, the triangles are similar.
cm3;
S 61.1
cm2
5. About 3.9 cm
6. About 357.3 cm2
8. PQR STR. Possible explanation: P S
and Q T because each pair is inscribed in the
same arc, so by the AA Similarity Conjecture, the
triangles are similar.
7. 9 quarts
LESSON 11.1 • Similar Polygons
1. AP 8 cm; EI 7 cm; SN 15 cm; YR 12 cm
2. SL 5.2 cm; MI 10 cm; mD 120°;
mU 85°; mA 80°
3. Yes. All corresponding angles are congruent. Both
figures are parallelograms, so opposite sides within
each parallelogram are equal. The corresponding
sides are proportional 155 93.
4. Yes. Corresponding angles are congruent by the CA
Conjecture. Corresponding sides are proportional
2
3
4
4 = 6 = 8.
6
8
5. No. 1
8 22 .
6. Yes. All angles are right angles, so corresponding
angles are congruent. The corresponding side
lengths have the ratio 47, so corresponding side
lengths are proportional.
1
7. 2
y
4
A(0, 1)
LESSON 11.3 • Indirect Measurement with
Similar Triangles
1. 27 ft
2. 6510 ft
4. About 18.5 ft
5. 0.6 m, 1.2 m, 1.8 m, 2.4 m, and 3.0 m
LESSON 11.4 • Corresponding Parts of Similar Triangles
1. h 0.9 cm; j 4.0 cm
2. 3.75 cm, 4.50 cm, 5.60 cm
5
3. WX 137 13.7 cm; AD 21 cm; DB 12 cm;
6
YZ 8 cm; XZ 67 6.9 cm
50
80
4. x 1
3 3.85 cm; y 13 6.15 cm
6. CB 24 cm; CD 5.25 cm; AD 8.75 cm
C(1.5, 1.5)
D(2, 0.5)
x
4
LESSON 11.5 • Proportions with Area
1. 5.4 cm2
2. 4 cm
25
5. 4
6. 16:25
9. 1296 tiles
y
D (2, 4)
5
x
LESSON 11.2 • Similar Triangles
1. MC 10.5 cm
2. Q X; QR 4.8 cm; QS 11.2 cm
3. A E; CD 13.5 cm; AB 10 cm
4. TS 15 cm; QP 51 cm
5. AA Similarity Conjecture
ANSWERS
9
3. 2
5
7. 2:3
36
4. 1
8
8. 8889 cm2
LESSON 11.6 • Proportions with Volume
E(8, 2)
F(4, 2)
112
3. 110.2 mi
5. a 8 cm; b 3.2 cm; c 2.8 cm
B (2, 3)
8. 4 to 1
5
9. MLK NOK. Possible explanation:
MLK NOK by CA and K K because
they are the same angle, so by the AA Similarity
Conjecture, the two triangles are similar.
3. 16 cm3
1. Yes
2. No
5. 8:125
6. 6 ft2
4. 20 cm
LESSON 11.7 • Proportional Segments Between
Parallel Lines
1. x 12 cm
2. Yes
3. No
4. NE 31.25 cm
5. PR 6 cm; PQ 4 cm; RI 12 cm
6. a 9 cm; b 18 cm
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7. RS 22.5 cm, EB 20 cm
7. About 24°
8. x 20 cm; y 7.2 cm
16
8
9. p 3 5.3 cm; q 3 2.6 cm
9. About 34.7 in.
LESSON 12.5 • Problem Solving with Trigonometry
LESSON 12.1 • Trigonometric Ratios
1. About 2.85 mi/h; about 15°
p
1. sin P r
p
3. tan P q
q
2. cos P r
q
4. sin Q r
5. sin T 0.800
6. cos T 0.600
7. tan T 1.333
8. sin R 0.600
9. x 12.27
10. x 29.75
11. x 18.28
8. About 43.0 cm
12. mA 71°
13. mB 53°
14. mC 30°
w
15. sin 40° 2;
8 w 18.0 cm
x
16. sin 28° 1;
4 x 7.4 cm
3 y 76.3 cm
17. cos 17° 7y;
18. a 28°
19. t 47°
20. z 76°
2. mA 50.64°, mB 59.70°, mC 69.66°
3. About 8.0 km from Tower 1, 5.1 km from Tower 2
4. About 853 miles
5. About 530 ft of fencing; about 11,656 ft2
LESSON 13.1 • The Premises of Geometry
1. a.
b.
c.
d.
e.
Given
Distributive property
Subtraction property
Addition property
Division property
2. False
M
LESSON 12.2 • Problem Solving with Right Triangles
A
1. Area 2 cm2
2. Area 325 ft2
3. Area 109 in2
4. x 54.0°
5. y 31.3°
6. a 7.6 in.
7. Diameter 20.5 cm
8. 45.2°
9. 28.3°
10. About 2.0 m
11. About 445.2 ft
12. About 22.6 ft
LESSON 12.3 • The Law of Sines
1. Area 46 cm2
2. Area 24 m2 3. Area 45 ft2
4. m 14 cm
5. p 17 cm
B
3. False
D
A
B
P
4. True; transitive property of congruence and
definition of congruence
5.
AB CD
ABP CDQ
Given
CA Postulate
6. q 13 cm
7. mB 66°, mC 33°
PB QD
ABP CDQ
Given
ASA Postulate
8. mP 37°, mQ 95°
AP CQ
APB CQD
AB CD
9. mK 81°, mM 21°
Given
CA Postulate
CPCTC
10. Second line: about 153 ft, between tethers: about 135 ft
LESSON 13.2 • Planning a Geometry Proof
LESSON 12.4 • The Law of Cosines
1. t 13 cm
2. b 67 cm
Proofs may vary.
1. Flowchart Proof
3. w 34 cm
AB CD
ABP CDQ
4. mA 76°, mB 45°, mC 59°
Given
CA Postulate
PAB QCD
AP CQ
APQ CQD
Third Angle
Theorem
Given
CA Postulate
5. mA 77°, mP 66°, mS 37°
6. mS 46°, mU 85°, mV 49°
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ANSWERS
113