Name ———————————————————————
LESSONS
6.4–6.7
Date ————————————
Problem Solving:
Mixed Problem Solving
For use with pages 399–431
has vertices A(23, 2), B(4, 2), C(4, 23), and
D(23, 23).
a. Draw rectangle ABCD. Then draw a
dilation of rectangle ABCD using
9
a scale factor of }5 . Label the image
EFGH.
b. Find the ratio of the perimeter of the
image to the perimeter of the original
figure. How does this ratio compare to
the scale factor?
c. Find the ratio of the area of the image
to the area of the original figure. How
does this ratio compare to the scale
factor?
2. Multi-Step Problem John is standing
in his back yard and he decides to estimate
the height of a tree. He stands so that the
tip of his shadow coincides with the tip of
the tree’s shadow, as shown below. John is
70 inches tall. The distance from the tree to
John is 75 feet and the distance between the
tip of the shadows and John is 7 feet.
3. Gridded Response You buy a miniature
version of an American flag. The miniature
3
flag is 3}5 inches by 6 inches. The actual
dimensions of an American flag are 3 feet
by 5 feet. What is the scale factor of the
reduction? Write your answer as a decimal.
4. Short Response The diagram below is
the side view of a bookshelf with only one
}
shelf shown. Is the shelf along KM parallel
}
to the floor JN? Explain.
L
28 in.
36 in.
K
21 in.
M
J
30 in.
N
5. Open-Ended Choose one of the theorems
from Lesson 6.6 and write a problem you
can solve using the theorem. Then show how
to solve the problem.
6. Extended Response You leave your
house to go to the movie theater. You drive
due east 10 miles, due south 10.5 miles, and
due east again 4 miles.
A
Your
house
70 in.
7 ft
10 miles
B
S
Not drawn to scale
C
LESSON 6.7
a. What postulate or theorem can you
438
Geometry
Chapter 6 Resource Book
E
W
75 ft
use to show that the triangles in the
diagram are similar?
b. About how tall is the tree, to the
nearest foot?
c. Hollie is 64 inches tall. She stands
so that the tip of her shadow and the
tip of the tree’s shadow coincide, as
described above. Her shadow is 6 feet
long. How far is Hollie from the tree?
N
D
Movie
theater
4 miles E
a. Explain how to prove that
n ABC , n EDC.
b. Find BC.
c. Find AE, the distance between your
house and the movie theater.
Copyright © Holt McDougal. All rights reserved.
1. Multi-Step Problem Rectangle ABCD
Lesson 6.7, continued
3
3. L(0, 6), M 3, } , N(26, 3)
2
1
2
c. 70.5 ft 3. 0.1
y
LK
LM }
4. No; Because } Þ }, KM is not parallel
KJ
MN
L
N
R
M
1
x
1
4. L(29, 6), M(23, 9), N(3, 6)
y
Challenge Practice
1. A9(25.5, 0.5), B9(6, 1), C9(26, 1.5),
D9(25.5, 2) 2. J9(3, 21), K9(6, 12), L9(15, 12),
M9(18, 21), N9(10.5, 24) 3. A(1, 21), B(3, 3),
C(21, 1)
4. W(21, 8), X(4, 3), Y(21, 22), Z(26, 22)
M
N
R
P
ANSWERS
}
to JN. 5. Answers will vary.
6. a. Use the AA Similarity Postulate because
∠ ABD and ∠ EDC are right angles, and ∠ ACB
and ∠ ECD are vertical angles. b. 7.5 mi
c. 17.5 mi
P
L
2. a. AA Similarity Postulate b. 68 ft
}
22
x
2
1
5. } 6. 2 7. D(6, 2); E(2, 12)
3
Problem Solving Workshop:
Mixed Problem Solving
1. a.
F
A
B
Copyright © Holt McDougal. All rights reserved.
H
1. 5 2. 13 3. 2 4. 1 5. 3 6. 1
NICE BELT
x
2
D
Chapter Review Game
7. 21 8. 8
y
6
E
Ï2
2
5. a. 18 units; } b. 18 square units; }
1
1
}
Ï2
2
c. Sample answer: } Þ }
1
1
C
G
9
b. }; The ratio is the same as the scale factor.
5
81
c. }; The ratio is equal to the square of the
25
scale factor.
Geometry
Chapter 6 Resource Book
A77