LESSON 6.1
Skills Practice
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Big and Small
Dilating Triangles to Create Similar Triangles
Vocabulary
Define the term in your own words.
1. similar triangles
Problem Set
Rectangle L9M9N9P9 is a dilation___
of rectangle
LMNP. The center of dilation
is point Z. Use a metric ruler to
___ ____ ___ ____ ____ ____
____
determine the actual lengths of ZL , ZN , ZM , ZP , ZL9 , ZN9 , ZM9 , and ZP9 to the nearest tenth of a
ZL9 , ____
ZN9, ____
ZM9 , and ____
ZP9 as decimals.
centimeter. Then, express the ratios ____
ZL ZN ZM
ZP
1.
N'
P'
N
© Carnegie Learning
P
Z
6
M
M'
L
L'
ZL 5 2, ZN 5 3, ZM 5 3, ZP 5 2, ZL9 5 5, ZN9 5 7.5, ZM9 5 7.5, ZP9 5 5
5 5 2.5, ____
7.5 5 2.5, ____
7.5 5 2.5, ____
5 5 2.5
____
ZL9 5 __
ZN9 5 ___
ZM9 5 ___
ZP9 5 __
ZL
2
ZN
3
ZM
3
ZP
2
Chapter 6 Skills Practice
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LESSON 6.1
2.
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L
M
L'
P
M'
P'
N
N'
Z
L'
M
N
P
L
6
510
N'
M'
Z
Chapter 6
Skills Practice
P'
© Carnegie Learning
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LESSON 6.1
Skills Practice
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4.
Z
L
M'
P'
N'
M
N
© Carnegie Learning
P
L'
6
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LESSON 6.1
Skills Practice
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Given the image and pre-image, determine the scale factor.
5.
y
16
14
12
10
8
A´
6
4
A
C´
2
0
B´
B
C
2
4
6
8
10
12 14
16 x
The scale factor is 2.
Each coordinate of the image is two times the corresponding coordinate of the pre-image.
䉭ABC has vertex coordinates A(2, 3), B(5, 1), and C(2, 1).
䉭A9B9C9 has vertex coordinates A9(4, 6), B9(10, 2), and C9(4, 2).
6.
y
16
D´
14
12
10
8
6
D
F´
E´
4
0
F
E
2
4
6
8
10
12 14
6
512
Chapter 6
Skills Practice
16 x
© Carnegie Learning
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LESSON 6.1
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y
16
G
14
12
10
8
6
G´
H
I
4
2
0
8.
I´
H´
2
4
6
8
10
12 14
16 x
y
16
L
14
12
10
8
L´
© Carnegie Learning
6
J
K
4
2
J´
0
2
K´
4
6
8
10
12 14
6
16 x
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LESSON 6.1
Skills Practice
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Given the pre-image, scale factor, and center of dilation, use a compass and straight edge to graph
the image.
9. The scale factor is 3 and the center of dilation is the origin.
y
16
14
12
10
8
B´
6
4
2
A´
B
C
A
0
C´
2
4
6
8
10
12 14
16 x
10. The scale factor is 4 and the center of dilation is the origin.
y
16
14
12
10
8
6
4
A
2
B
C
0
2
4
6
10
8
12 14
16 x
11. The scale factor is 2 and the center of dilation is the origin.
© Carnegie Learning
y
8
6
7
6
5
4
F
3
2
D
E
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0
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7
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12. The scale factor is 5 and the center of dilation is the origin.
y
24
20
16
12
8
E
4
F
0 D
4
8
12
16
20
24
x
Use coordinate notation to determine the coordinates of the image.
13. nABC has vertices A(1, 2), B(3, 6), and C(9, 7). What are the vertices of the image after a dilation with
a scale factor of 4 using the origin as the center of dilation?
A(1, 2) → A9(4(1), 4(2)) 5 A9(4, 8)
B(3, 6) → B9(4(3), 4(6)) 5 B9(12, 24)
C(9, 7) → C9(4(9), 4(7)) 5 C9(36, 28)
© Carnegie Learning
14. nDEF has vertices D(8, 4), E(2, 6), and F(3, 1). What are the vertices of the image after a dilation with
a scale factor of 5 using the origin as the center of dilation?
15. nGHI has vertices G(0, 5), H(4, 2), and I(3, 3). What are the vertices of the image after a dilation with
a scale factor of 9 using the origin as the center of dilation?
6
16. nJKL has vertices J(6, 2), K(1, 3), and L(7, 0). What are the vertices of the image after a dilation with a
scale factor of 12 using the origin as the center of dilation?
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17. nABC has vertices A(8, 4), B(14, 16), and C(6, 10). What are the vertices of the image after a dilation
1 using the origin as the center of dilation?
with a scale factor of __
2
18. nDEF has vertices D(25, 25), E(15, 10), and F(20, 10). What are the vertices of the image after a
1 using the origin as the center of dilation?
dilation with a scale factor of __
5
19. nGHI has vertices G(0, 20), H(16, 24), and I(12, 12). What are the vertices of the image after a dilation
3 using the origin as the center of dilation?
with a scale factor of __
4
© Carnegie Learning
20. nJKL has vertices J(8, 2), K(6, 0), and L(4, 10). What are the vertices of the image after a dilation with
5 using the origin as the center of dilation?
a scale factor of __
2
6
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LESSON 6.2
Skills Practice
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Similar Triangles or Not?
Similar Triangle Theorems
Vocabulary
Give an example of each term. Include a sketch with each example.
1. Angle-Angle Similarity Theorem
© Carnegie Learning
2. Side-Side-Side Similarity Theorem
6
Chapter 6 Skills Practice
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LESSON 6.2
Skills Practice
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3. Side-Angle-Side Similarity Theorem
4. included angle
© Carnegie Learning
5. included side
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LESSON 6.2
Skills Practice
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Problem Set
Explain how you know that the triangles are similar.
1.
The triangles are congruent by the Angle-Angle Similarity Theorem. Two corresponding angles are
congruent.
2.
52°
83°
52° 83°
3.
4.5 ft
4.5 ft
3 ft
© Carnegie Learning
3 ft
2 ft
3 ft
6
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LESSON 6.2
Skills Practice
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4.
8 in.
8 in.
4 in.
4 in.
5 in.
10 in.
5.
6 cm
2 cm
60°
60°
3 cm
9 cm
6.
10 mm
40°
7 mm
6
520
Chapter 6
40°
14 mm
Skills Practice
© Carnegie Learning
5 mm
LESSON 6.2
Skills Practice
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Determine what additional information you would need to prove that the triangles are similar using the
given theorem.
7. What information would you need to use the Angle-Angle Similarity Theorem to prove that the
triangles are similar?
35°
60°
To prove that the triangles are similar using the Angle-Angle Similarity Theorem, the first triangle
should have a corresponding 60 degree angle and the second triangle should have a corresponding
35 degree angle.
8. What information would you need to use the Angle-Angle Similarity Theorem to prove that the
triangles are similar?
110°
35°
© Carnegie Learning
9. What information would you need to use the Side-Angle-Side Similarity Theorem to prove that the
triangles are similar?
6
6m
4m
10 m
Chapter 6 Skills Practice
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LESSON 6.2
Skills Practice
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10. What information would you need to use the Side-Angle-Side Similarity Theorem to prove that the
triangles are similar?
5 in.
5 in.
9 in.
9 in.
11. What information would you need to use the Side-Side-Side Similarity Theorem to prove that these
triangles are similar?
12 cm
6 cm
5 cm
14 cm
6
522
6 ft
4 ft
Chapter 6
Skills Practice
© Carnegie Learning
12. What information would you need to use the Side-Side-Side Similarity Theorem to prove that these
triangles are similar?
LESSON 6.2
Skills Practice
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Determine whether each pair of triangles is similar. Explain your reasoning.
13.
Y
10.8 yd
T
10 yd
R
6 yd
X
S
Z
18 yd
The triangles are similar by the Side-Angle-Side Similarity Theorem because the included angles
in both triangles are congruent and the corresponding sides are proportional.
10 5 __
5
___
XY 5 ___
6
3
RS
18 5 __
5
___
XZ 5 _____
RT
10.8
3
14.
K
B
8 cm
12 cm
16 cm
J
12 cm
L
C
© Carnegie Learning
A
6 cm
9 cm
6
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LESSON 6.2
Skills Practice
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N
15.
60°
2 in.
3 in.
M
O
Q
150°
7.5 in.
R
5 in.
P
16.
P
100°
20°
R
T
Q
100°
60°
U
6
524
Chapter 6
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© Carnegie Learning
S
LESSON 6.2
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17.
V
10 m
W
X
18 m
4.5 m
A
B
2.5 m
C
18.
K
5 ft
3 ft
L
J
6 ft
© Carnegie Learning
I
12 ft
10 ft
6
H
7 ft
G
Chapter 6 Skills Practice
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LESSON 6.2
19.
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O
M
N
R
P
Q
D
20.
15 m
E
18 m
F
27 m
S
U
6
526
T
Chapter 6
20 m
Skills Practice
© Carnegie Learning
24 m
36 m
LESSON 6.3
Skills Practice
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Keep It in Proportion
Theorems About Proportionality
Vocabulary
© Carnegie Learning
Match each definition to its corresponding term.
1. Angle Bisector/Proportional Side Theorem
a. If a line parallel to one side of a triangle intersects
the other two sides, then it divides the two sides
proportionally.
2. Triangle Proportionality Theorem
b. A bisector of an angle in a triangle divides the
opposite side into two segments whose lengths are
in the same ratio as the lengths of the sides
adjacent to the angle.
3. Converse of the Triangle
Proportionality Theorem
c. If a line divides two sides of a triangle proportionally,
then it is parallel to the third side.
4. Proportional Segments Theorem
d. The midsegment of a triangle is parallel to the third
side of the triangle and half the measure of the third
side of the triangle
5. Triangle Midsegment Theorem
e. If three parallel lines intersect two transversals, then
they divide the transversals proportionally.
Chapter 6 Skills Practice
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LESSON 6.3
Skills Practice
page 2
Problem Set
Calculate the length of the indicated segment in each figure.
___
___
1. HJ bisects /H. Calculate HF.
15 cm
F
J
2. LN bisects /L. Calculate NM.
L
18 cm
8 in.
G
21 cm
K
4 in.
5 in.
M
N
H
The length of segment HF is 17.5 centimeters.
GH 5 ___
GJ
____
HF
JF
18
___
21 5 ___
HF
15
18 ? HF 5 315
HF 5 17.5
___
3. BD bisects /B. Calculate AD.
C
___
4. SQ bisects /S. Calculate SP.
P
3 ft
9m
Q
2 ft
D
6 ft
A
6
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Chapter 6
Skills Practice
12 m
S
18 m
R
© Carnegie Learning
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LESSON 6.3
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___
___
5. YZ bisects /Y. Calculate YW.
6. VX bisects /V. Calculate XW.
Y
U
9 ft
4 cm
X
8 cm
V
W
9 cm
Z
6 ft
X
10 ft
W
___
___
7. GE bisects /G. Calculate FD.
8. ML bisects /M. Calculate NL.
N
D
5 cm
15 cm
E
11 mm
L
5 mm
© Carnegie Learning
G
18 cm
F
K
4 mm
M
6
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LESSON 6.3
Skills Practice
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Use the given information to answer each question.
9. On the map shown, Willow Street bisects the angle formed by Maple Avenue and South Street. Mia’s
house is 5 miles from the school and 4 miles from the fruit market. Rick’s house is 6 miles from the
fruit market. How far is Rick’s house from the school?
Mia’s house
Willow Street
Fruit market
Maple Avenue
Rick’s house
School
River Avenue
South Street
Rick’s house is 7.5 miles from the school.
__5 5 _x_
4
6
4x 5 30
x 5 7.5
10. Jimmy is hitting a golf ball towards the hole. The line from Jimmy to the hole bisects the angle formed
by the lines from Jimmy to the oak tree and from Jimmy to the sand trap. The oak tree is 200 yards
from Jimmy, the sand trap is 320 yards from Jimmy, and the hole is 250 yards from the sand trap.
How far is the hole from the oak tree?
6
530
Oak tree
Chapter 6
Hole
Skills Practice
Sand trap
© Carnegie Learning
Jimmy
LESSON 6.3
Skills Practice
page 5
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11. The road from Central City on the map shown bisects the angle formed by the roads from Central
City to Minville and from Central City to Oceanview. Central City is 12 miles from Oceanview, Minville
is 6 miles from the beach, and Oceanview is 8 miles from the beach. How far is Central City from
Minville?
Minville
Beach
Central City
Oceanview
12. Luigi is racing a remote control car from the starting point to the winner’s circle.That path bisects the
angle formed by the lines from the starting point to the house and from the starting point to the
retention pond. The house and the retention pond are each 500 feet from the starting point. The
house is 720 feet from the retention pond. How far is the winner’s circle from the retention pond?
Starting point
Winner’s circle
Retention pond
© Carnegie Learning
House
6
Chapter 6 Skills Practice
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LESSON 6.3
Skills Practice
page 6
Use the diagram and given information to write a statement that can be justified using the Proportional
Segments Theorem, Triangle Proportionality Theorem, or its Converse. State the theorem used.
A
13.
B
14.
D
E
B
C
Q
A
___
AE , Triangle Proportionality Theorem
AD 5 ___
DB
15.
P
C
EC
A
16.
L1
x
a
L2
24
y
18
b
L3
E
D
8
C
A
17.
B
E
18.
3 cm
P
6
Q
P
3.9 cm
B
532
Chapter 6
C
Skills Practice
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2.4 cm Q
3.6 cm
D
© Carnegie Learning
6
LESSON 6.3
Skills Practice
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19.
20.
E
9
5
2.5
H
F
G
I
2
G
F
H
A
B
C
D
E
Use the Triangle Proportionality Theorem and the Proportional Segments Theorem to determine the
missing value.
Q
21.
2 S
22.
6
P
4
9
6
R
x
6
x
T
__x 5 __2
9
6
6x 5 18
© Carnegie Learning
x53
6
Chapter 6 Skills Practice
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LESSON 6.3
Skills Practice
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A
24.
23.
8x ⫺ 7
4x ⫺ 3
4.4
D
14.08
E
5x ⫺ 3
3x ⫺ 1
6.3
x
B
C
Use the diagram and given information to write two statements that can be justified using the Triangle
Midsegment Theorem.
26.
B
D
R
E
A
V
C
T
6
Given: ABC is a triangle
D is the midpoint of AB
__
Chapter 6
Skills Practice
S
Given: RST is a triangle
___
of BC
___ ___E is the midpoint
1
DE i AC , DE 5 AC
2
534
W
___
V is the midpoint of RT
___
W is the midpoint of RS
© Carnegie Learning
25.
LESSON 6.3
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Y
M
28.
N
X
X
U
P
Z
T
Y
Given: MNP is a triangle
Given: XYZ is a triangle
____
___
X is the midpoint of MP
T is the midpoint of YZ
____
___
Y is the midpoint of MN
U is the midpoint of XY
Given each diagram, compare the measures described. Simplify your answers, but do not evaluate
any radicals.
29. The
sides of triangle___
LMN have midpoints O(0, 0), P(29, 23), and Q(0, 23). Compare the length of
___
OP to the length of LM .
y
8
6
4
2
N
M
O
–8
–6
–4
–2
0
–2
P
2
4
6
8
x
Q
–4
L
–6
© Carnegie Learning
–8
Segment LM is two times the length of segment OP.
6
____________________
OP 5 √(29 2 0)2 1 (23 2 0)2
_____________
_______
5 √(29)2 1 (23)2 5 √ 81 1 9
___
___
5 √90 5 3√10
_______________________
LM 5 √ (10 2 (28)2 1 (0 2 (26))2
________
_________
5 √182 1 62 5 √324 1 36
____
___
5 √360 5 6√ 10
Chapter 6 Skills Practice
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LESSON 6.3
Skills Practice
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___
30. The sides of triangle
LMN have midpoint P(0, 0), Q(22, 2), and R(2, 2). Compare the length of QP to
___
the length of LN .
y
4
L
3
(–2, 2)
Q
2
(2, 2)
R
1
M
–4
–3
–2
–1
P 1
–1 (0, 0)
2
3
4
x
N
–2
–3
© Carnegie Learning
–4
6
536
Chapter 6
Skills Practice
LESSON 6.4
Skills Practice
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Geometric Mean
More Similar Triangles
Vocabulary
Write the term from the box that best completes each statement.
Right Triangle/Altitude Similarity Theorem
geometric mean
Right Triangle Altitude/Hypotenuse Theorem
Right Triangle Altitude/Leg Theorem
states that if an altitude is drawn to the
1. The
hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to
each other.
2. The
states that if the altitude is drawn to the
hypotenuse of a right triangle, each leg of the right triangle is the geometric mean of the measure of
the hypotenuse and the measure of the segment of the hypotenuse adjacent to the leg.
of two positive numbers a and b is the positive
3. The
a 5 __
x
number x such that __
x b.
states that the measure of the altitude drawn
4. The
from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between
the measures of the two segments of the hypotenuse.
Problem Set
Construct an altitude to the hypotenuse of each right triangle.
© Carnegie Learning
1.
2.
K
O
6
M
J
L
N
Chapter 6 Skills Practice
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LESSON 6.4
Skills Practice
3.
page 2
4.
U
Q
V
T
S
R
Use each similarity statement to write the corresponding sides of the triangles as proportions.
5. nCGJ , nMKP
CG 5 GJ 5 CJ
MK KP MP
6. nXZC , nYMN
7. nADF , nGLM
8. nWNY , nCQR
____ ___ ____
Use the Right Triangle/Altitude Similarity Theorem to write three similarity statements involving the
triangles in each diagram.
9.
H
10.
M
P
R
Q
Z
G
P
© Carnegie Learning
nHPG , nPQG, nHPG , nHQP,
nPQG , nHQP
6
11.
12.
N
K
L
W
T
U
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Chapter 6
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N
LESSON 6.4
Skills Practice
page 3
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Solve for x.
13.
B
x
R
20 cm
T
14.
D
x
8 cm
A
6 in.
F
6 in.
G
F
___
FB 5 ___
RB
TB
FB
___8 5 __x
20
8
20x 5 64
x 5 3.2 cm
15.
M
x
16.
9 in.
R
S
Z
12 cm
6 in.
4 cm
Q
N
P
x
© Carnegie Learning
V
6
Chapter 6 Skills Practice
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LESSON 6.4
17.
Skills Practice
page 4
18.
B
G
x
4m
K
4 mi
L
D
25 mi
T
10 m
F
x
L
Solve for x, y, and z.
19.
W
C
25
CP 5 ____
____
WP
WP
PH
25 5 __
___
x
x
4
540
H
x2 1 252 5 y2
42 1 x2 5 z2
100 1 625 5 y2
16 1 100 5 z2
725 5 y
___
x 5 10
Chapter 6
P 4
2
x2 5 100
6
z
x
5√ 29 5 y
Skills Practice
116 5 z2
___
2√ 29 5 z
© Carnegie Learning
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LESSON 6.4
Skills Practice
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20.
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B
x
3
V
15
y
21.
Y
z
R
K
y
z
8
4 N
x
P
© Carnegie Learning
L
6
Chapter 6 Skills Practice
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LESSON 6.4
22.
Skills Practice
page 6
K
4
5
H
y
A
x
z
T
Use the given information to answer each question.
23. You are on a fishing trip with your friends. The diagram shows the location of the river, fishing hole,
camp site, and bait store. The camp site is located 200 feet from the fishing hole. The bait store is
located 110 feet from the fishing hole. How wide is the river?
Camp site
6
The river is 60.5 feet wide.
200 5 ____
110
____
x
110
200x 5 12,100
x 5 60.5
542
Chapter 6
Skills Practice
© Carnegie Learning
Fishing
hole
River
Bait store
LESSON 6.4
Skills Practice
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24. You are standing at point D in the diagram looking across a bog at point B. Point B is 84 yards from
point A and 189 yards from point C. How wide across is the bog?
A
D
B
Bog
C
25. Marsha wants to walk from the parking lot through the forest to the clearing, as shown in the
diagram. She knows that the forest ranger station is 154 feet from the flag pole and the flag pole is
350 feet from the clearing. How far is the parking lot from the clearing?
Clearing
© Carnegie Learning
Flag pole
Forest
ranger
station
t
es
r
Fo
6
Parking lot
Chapter 6 Skills Practice
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LESSON 6.4
Skills Practice
page 8
26. Andre is camping with his uncle at one edge of a ravine. The diagram shows the location of their tent.
The tent is 1.2 miles from the fallen log and the fallen log is 0.75 miles from the observation tower.
How wide is the ravine?
Ravine
Tent
6
544
Fallen log
© Carnegie Learning
Observation
tower
Chapter 6
Skills Practice
LESSON 6.5
Skills Practice
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Proving the Pythagorean Theorem
Proving the Pythagorean Theorem and
the Converse of the Pythagorean Theorem
Problem Set
Write the Given and Prove statements that should be used to prove the indicated theorem using
each diagram.
1. Prove the Pythagorean Theorem.
2. Prove the Converse of
the Pythagorean Theorem.
D
C
B
A
F
Given: nABC with right angle C
Given:
Prove: AC 1 BC 5 AB
Prove:
2
2
2
3. Prove the Pythagorean Theorem.
X
w
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E
v
W
V
v
w
Q
v
x
x
x
w
4. Prove the Pythagorean Theorem.
x
w
P
6
v
S
Given:
Given:
Prove:
Prove:
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LESSON 6.5
Skills Practice
5. Prove the Pythagorean Theorem.
h
G
g
U
t
g
g
H
f
g
6. Prove the Converse of
the Pythagorean Theorem.
F
f
f⫺
h
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f
s
S
h
u
T
g
h
Given:
Given:
Prove:
Prove:
Prove each theorem for the diagram that is given. Use the method indicated. In some cases, the proof has
been started for you.
7. Prove the Pythagorean Theorem using similar triangles.
Draw an altitude to the hypotenuse at point N.
K
N
L
According to the Right Triangle/Similarity
Theorem, nKLM , nLMN , nMKN.
According to the definition of similar triangles, the sides of similar
triangles are proportional.
KL 5 KM
KM
KN
KM2 5 KL 3 KN
M
____ ____
____
KL 5 ____
ML
ML
NL
ML2 5 KL 3 NL
KM2 1 ML2 5 KL 3 KN 1 KL 3 NL
KM2 1 ML2 5 KL(KL)
KM2 1 ML2 5 KL2
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KM2 1 ML2 5 KL(KN 1 NL)
LESSON 6.5
Skills Practice
page 3
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8. Prove the Pythagorean Theorem using algebraic reasoning.
n
m
n
m
n
s
s
s
s
m
m
n
9. Prove the Converse of the Pythagorean Theorem using algebraic reasoning and the SSS Theorem.
R
Construct a right triangle that has legs the same
lengths as the original triangle, q and r, opposite
angles Q and R. Label the hypotenuse of this
triangle t, opposite the right angle T.
q
s
r
Q
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LESSON 6.5
Skills Practice
page 4
10. Prove the Pythagorean Theorem using similarity.
h
m
m
k
k⫺
h
m
k
k
k
m
h
m
h
11. Prove the Converse of the Pythagorean Theorem using algebraic reasoning.
Construct a right triangle that shares side h with the
original triangle and has one leg length g, as in the
original triangle, and the other leg length w.
g
h
G
g
w
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f
H
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Skills Practice
LESSON 6.5
Skills Practice
page 5
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12. Prove the Pythagorean Theorem using similar triangles.
Given: nABC with right angle C
A
Place side a along the diameter of a circle of radius c
so that B is at the center of the circle.
b
c⫺a
a
C
c
B
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D
c
E
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Skills Practice
LESSON 6.6
Skills Practice
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Indirect Measurement
Application of Similar Triangles
Vocabulary
Provide an example of the term.
1. indirect measurement
Problem Set
Explain how you know that each pair of triangles are similar.
1.
A
B
C
D
E
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The angles where the vertices of the triangle intersect are vertical angles, so angles /ACB and
/ECD are congruent. The angles formed by BD intersecting the two parallel lines are right angles,
so they are also congruent. So by the Angle-Angle Similarity Theorem, the triangles formed
are similar.
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LESSON 6.6
Skills Practice
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F
2.
H
G
J
I
3.
6 in.
3 in.
8 in.
4.
4 in.
B
A
C
E
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Use indirect measurement to calculate the missing distance.
5. Elly and Jeff are on opposite sides of a canyon that runs east to west, according to the graphic. They
want to know how wide the canyon is. Each person stands 10 feet from the edge. Then, Elly walks
24 feet west, and Jeff walks 360 feet east.
24 ft
10 ft
10 ft
360 ft
What is the width of the canyon?
The distance across the canyon is 140 feet.
10 1 x 5 ____
360
_______
10
24
10 1 x 5 150
x 5 140
6. Zoe and Ramon are hiking on a glacier. They become separated by a crevasse running east to west.
Each person stands 9 feet from the edge. Then, Zoe walks 48 feet east, and Ramon walks 12 feet
west.
48 ft
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9 ft
9 ft
12 ft
6
What is the width of the crevasse?
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LESSON 6.6
Skills Practice
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7. Minh wanted to measure the height of a statue. She lined herself up with the statue’s shadow so that
the tip of her shadow met the tip of the statue’s shadow. She marked the spot where she was
standing. Then, she measured the distance from where she was standing to the tip of the shadow,
and from the statue to the tip of the shadow.
Minh
5 ft
12 ft
84 ft
What is the height of the statue?
8. Dimitri wants to measure the height of a palm tree. He lines himself up with the palm tree’s shadow
so that the tip of his shadow meets the tip of the palm tree’s shadow. Then, he asks a friend to
measure the distance from where he was standing to the tip of his shadow and the distance from the
palm tree to the tip of its shadow.
Dimitri
45 ft
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11.25 ft
What is the height of the palm tree?
Chapter 6
Skills Practice
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6 ft
LESSON 6.6
Skills Practice
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9. Andre is making a map of a state park. He finds a small bog, and he wants to measure the distance
across the widest part. He first marks the points A, C, and E. Andre measures the distances shown
on the image. Andre also marks point B along AC and point D along AE, such that BD is parallel
to CE.
A
14 ft
D
B
12 ft
126 ft
C
E
What is the width of the bog at the widest point?
10. Shira finds a tidal pool while walking on the beach. She wants to know the maximum width of the
tidal pool. Using indirect measurement, she begins by marking the points A, C, and E. Shira
measures the distances shown on the image. Next, Shira marks point B along AC and point D along
AE, such that BD is parallel to CE.
A
B
7 ft
D
3 ft
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31.5 ft
C
6
E
What is the distance across the tidal pool at its widest point?
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LESSON 6.6
Skills Practice
page 6
11. Keisha is visiting a museum. She wants to know the height of one of the sculptures. She places a
small mirror on the ground between herself and the sculpture, then she backs up until she can see
the top of the sculpture in the mirror.
x
5.5 ft
19.2 ft
13.2 ft
What is the height of the sculpture?
12. Micah wants to know the height of his school. He places a small mirror on the ground between
himself and the school, then he backs up until he can see the highest point of the school in the mirror.
x
6 ft
93.5 ft
12.75 ft
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What is the height of Micah’s school?
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