000200010271960393 unit3 inv1-4 p055-079.qxd 11/21/15 4:13 ... · 000200010271960393 unit3 inv1-4...
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d.
Name ____________________________________________ Date ____________ Class ____________
Additional PracticeStretching and Shrinking
Investigation 1
1. Refer to the rectangle at the right for the exercises below.
a. Give the length and width of a larger similar rectangle.
Explain your reasoning.
b. Give the length and width of a smaller similar rectangle. Explain your
reasoning.
c. Give the length and width of a rectangle that is not similar to this one.
Explain your reasoning.
4 cm
3 cm
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Investigation 1
Name ____________________________________________ Date ____________ Class ____________
Additional Practice (continued)
Stretching and Shrinking
2. Figure VWXYZ is an enlargement of figure ABCDE. Name all the pairs of
corresponding sides and all the pairs of corresponding angles of the two
figures.
3. a. Draw a square. Then draw a square with a side length that is twice the side
length of the original square. How many copies of the smaller square will
fit inside the larger square?
b. Will you get the same answer for part (a) no matter what side length you
choose for the original square? Explain your reasoning.
A
Y
X
W
V
Z
B
CD
E
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d.Investigation 1
4. a. Carl made shape B by making a photocopy of
shape A. What percent did he enter in the copier?
b. Amy made a photocopy of shape A by entering 250% into the photocopier.
Sketch the copy she got.
Shape A Shape B
Name ____________________________________________ Date ____________ Class ____________
Additional Practice (continued)
Stretching and Shrinking
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Name ____________________________________________ Date ____________ Class ____________
Additional Practice: Digital AssessmentsStretching and Shrinking
Investigation 1
5. Figure ABCDEF is similar to figure
UVWXYZ. Which of the following
statements are definitely true? Select all that apply.
D
E
F
C
A
B Y
X
W
V
U
Z
n Angle A corresponds to angle U.
n Angle C is congruent to angle W.
n Angle B corresponds to angle Y.
n Side DE corresponds to side XY.
n Side FE is the same length as side WX.
6. Which of the following are equivalent to 5 __ 8 ?
Select all that apply.
n 10
___ 16
n 7 ___
10
n 15
___ 24
n 0.625
n 0.0625
7. Use the tiles to show one way to find 30% of 92.
92
0.30
27.6
276
30
0.92
3
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d.Investigation 1
Name ____________________________________________ Date ____________ Class ____________
Skill: Using PercentStretching and Shrinking
Find the given percent of each number. Show your work.
1. 20% of 560 2. 42% of 200 3. 9% of 50
4. 40% of 70 5. 25% of 80 6. 50% of 80
7. 40% of 200 8. 5% of 80 9. 75% of 200
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Name ____________________________________________ Date ____________ Class ____________
Additional PracticeStretching and Shrinking
Investigation 2
1. Draw any rectangle that is not a square. Draw a similar rectangle by applying
a scale factor of 3 to the original rectangle.
a. How many copies of the original rectangle will fit inside the new rectangle?
b. Will you get the same answer for part (a) no matter what rectangle you use
as the original rectangle?
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d.Investigation 2
Name ____________________________________________ Date ____________ Class ____________
Additional Practice (continued)
Stretching and Shrinking
2. Make a figure by connecting the following sets of points on the coordinate grid:
Set 1: (8, 5), (8, 8), (0, 8), (0, 5), (8, 5) Set 2: (4, 6), (8, 2), (0, 2), (4, 6)
Set 3: (2, 6), (1, 6), (1, 7), (2, 7), (2, 6) Set 4: (6, 6), (7, 6), (7, 7), (6, 7), (6, 6)
a. Suppose you used the rule (6x, 6y) to transform this figure into a new
figure. How would the angles of the new figure compare with the angles of
the original? How would the side lengths compare? Would the new figure
be similar to the original? Explain.
b. Suppose you used the rule (3x�1, 3y�4) to transform the original figure
into a new figure. Would the new figure be similar to the original? Explain.
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Investigation 2
Name ____________________________________________ Date ____________ Class ____________
Additional Practice (continued)
Stretching and Shrinking
3. Recall that Zug Wump was made from Mug Wump using a scale factor of 2.
What is the scale factor from Zug to Mug? Explain.
4. a. Wendy drew a very large Wump using the rule (8x, 8y). She said that the
scale factor from Mug to her Wump was 8 and that the scale factor from
Zug to her Wump was 4. Do you agree with Wendy? Explain.
b. Wendy could not figure out the scale factor from Bug Wump to her new
large Wump. What is this scale factor? (Hint: Applying the rule (3x, 3y) to
Mug creates Bug.)
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Name ____________________________________________ Date ____________ Class ____________
Additional Practice: Digital AssessmentsStretching and Shrinking
Investigation 2
5. The original figure below is transformed
using the rule (x 2 1, 2y).
y
O 4
2
4
�2�4
�2
�4
x
Which of these points are vertices of the
new transformed figure? Select all that apply.
n (2, 0)
n (2, 21)
n (21, 24)
n (23, 0)
n (23, 21)
n (1, 0)
n (21, 4)
6. Write the letter for each pair of figures in the correct box.
A B DCA B DC
A B DCA B DC
Similar Figures Not Similar Figures
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Investigation 2
Name ____________________________________________ Date ____________ Class ____________
Skill: Similar FiguresStretching and Shrinking
Tell whether the triangles are similar.
1. 2. 3.
4. List the pairs of figures that appear to be similar.
a. b. c. d.
e. f. g. h.
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d.Investigation 2
For Exercises 5 and 6, graph quadrilateral ABCD. Then graph its imageA�B�C�D� with the given scale factor.
5. A(2, �2), B(3, 2), C(�3, 2), D(�2, �2); scale factor 2
6. A(6, 3), B(0, 6), C(�6, 2), D(�6, �5); scale factor 12
Name ____________________________________________ Date ____________ Class ____________
Skill: Similar Figures (continued)
Stretching and Shrinking
O�4�6 4 6x
y
�2
�4
�6
�2 2
6
4
2
O�4�6 4 6x
y
�2
�4
�6
�2 2
6
4
2
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Investigation 2
Name ____________________________________________ Date ____________ Class ____________
Skill: Similar Figures (continued)
Stretching and Shrinking
7. Quadrilateral A�B�C�D� is similar to quadrilateral ABCD. Find the scale factor
from ABCD to A�B�C�D�.
O�4�6 4 6x
y
�2
�4
�6
�2 2
6
4
2
A
D
B
B �
A�C �
D �
C
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Name ____________________________________________ Date ____________ Class ____________
Additional PracticeStretching and Shrinking
Investigation 3
1. On the grid below, make a right triangle with legs of length 8 and 12.
a. Give the leg lengths of two smaller right triangles that are similar to the
one you drew and that have whole-number side lengths.
b. Copies of each smaller triangle can be put together to exactly match the
original triangle. How many of each smaller triangle does it take to match
the original?
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Investigation 3
Name ____________________________________________ Date ____________ Class ____________
Additional Practice (continued)
Stretching and Shrinking
2. In the grid below, each unit represents 1 centimeter. On the grid, make an
isosceles triangle with base and height both equal to 6 centimeters.
a. Can isosceles triangles with base and height equal to 2 centimeters be put
together to exactly match the shape of the original triangle? Is each smaller
triangle similar to the original?
b. Can isosceles triangles with base and height equal to 4 centimeters be put
together to exactly match the shape of the original triangle? Is each smaller
triangle similar to the original?
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d.Investigation 3
3. Find the missing side lengths in each pair of similar figures below.
a.
b.
4. For each pair of similar figures below, give the scale factor from figure A to
figure B.
a. b.
c.
A
B
A
B
A B
x
6 cm
2 cm 2 cm 4 cm 4 cm
8 cmx
3 cm 2 cm
Name ____________________________________________ Date ____________ Class ____________
Additional Practice (continued)
Stretching and Shrinking
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Investigation 3
Name ____________________________________________ Date ____________ Class ____________
Additional Practice (continued)
Stretching and Shrinking
5. a. The drawing below shows how a square foot and a square yard compare.
How many square feet are in a square yard? Explain your reasoning.
b. Are a square foot and a square yard similar? If so, what is the scale factor
from a square foot to a square yard? What is the scale factor from a square
yard to a square foot?
c. Compare a square inch with a square foot. What is the scale factor from a
square inch to a square foot?
d. How many square inches are in a square foot? Explain.
e. Compare a square inch with a square yard. What is the scale factor from a
square inch to a square yard?
f. How many square inches are in a square yard?
1 yd1 ft
1 ft
1 yd
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Name ____________________________________________ Date ____________ Class ____________
Additional Practice: Digital AssessmentsStretching and Shrinking
Investigation 1Investigation 3
6. The figures below are similar. Use the
values in the bank to label the missing side
lengths.
12 15 16.5 18 32.5 36
12.5
30
135
7. The two pentagons below are similar.
Complete the missing side lengths using the
values in the bank.
1 __ 3 in. 2 __
3 in. 4 __
3 in. 1 in. 2 in. 3 in. 4 in.
6 in.
2 in.
2 in.
1 in.
in.43
in.43
8. Triangle ABC is similar to triangle A9B9C9. Circle the numbers that make the statements true.
The scale factor from triangle ABC to
triangle A9B9C9 is
Q 2 4
1 __ 2
1 __ 4
U because the coordinates of
each vertex are multiplied by Q 2 4
1 __ 2
1 __ 4
U .y
O 2 31
1
2
3
4
�2�4
�1
�2
�3
A�
B�
C� C
A
B
x
9. Rectangle A is a transformation of rectangle B, scaled by a factor of 4.
How many copies of rectangle B can fit inside rectangle A?
~ 2 ~ 4 ~ 8 ~ 16
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Investigation 3
Name ____________________________________________ Date ____________ Class ____________
Skill: Similar PolygonsStretching and Shrinking
The pairs of figures below are similar. Find the value of each variable.
1. 2.
3. 4.
5. 6. 15
9
6x8
4
5
x
20
15
10 8
y
xx
20
6
14
24 18
16y
5 5
5 5
5
4 x
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d.Investigation 3
Name ____________________________________________ Date ____________ Class ____________
Skill: Fractions, Decimals, and PercentsStretching and Shrinking
Write three equivalent fractions for each fraction.
1. 2.
3. 4.
5. 6.
7. 8.
Write each fraction as a decimal and as a percent.
9. 10.
11. 12. 1720
1325
710
35
832
1545
812
1520
34
56
78
310
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1. a. Rachel was working with the triangles below:
She wrote the fraction . What was she thinking about?
b. Next, she wrote the fraction while working with these two triangles:
Was she thinking in the same way or differently? Explain.
3 cm
9 cm18 cm
6 cm
13
12
2 cm
4 cm
4 cm 8 cm
74
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Name ____________________________________________ Date ____________ Class ____________
Additional PracticeStretching and Shrinking
Investigation 4
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d.Investigation 4
Name ____________________________________________ Date ____________ Class ____________
Additional Practice (continued)
Stretching and Shrinking
2. Below are several pairs of similar figures. In each, find the missing
measurement(s).
a.
b.
c.
2.5 cm
5 cm 6.495 cm4.33 cm e
d
1.5 cm
10 cm
2.5 cm
b 5 cm
c
3 cm
4 cm 7.5 cm
a
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Investigation 4
Name ____________________________________________ Date ____________ Class ____________
Additional Practice (continued)
Stretching and Shrinking
3. In each figure below, find the missing measurement.
a.
b.
1.96 cm25 cm
y
6.72 cm 7 cm
1.8 cm5 cm
3 cm2.4 cm
x
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Name ____________________________________________ Date ____________ Class ____________
Additional Practice: Digital AssessmentsStretching and Shrinking
Investigation 4
4. Using the values from the bank, find the
missing measurement.
5 cm 6 cm 10 cm 12 cm 18 cm
3 cm6 cm
5. Which statements about the figures are
true? Select all that apply.
2.4 cm1.2 cm 1.0 cm
3.0 cm1.6 cm
6.0 cm
2.0 cm
3.2 cm
A
E
F
G
HB
C
D
2.4 cm1.2 cm 1.0 cm
3.0 cm1.6 cm
6.0 cm
2.0 cm
3.2 cm
A
E
F
G
HB
C
D
n ABCD is similar to EFGH.
n Side AB is congruent to side EF.
n Side DC corresponds to side HG.
n The ratio of side AB to side AD is the
same as the ratio of side EF to side EH.
n The scale factor from ABCD to EFGH
is 2.
6. Jaqué wants to calculate the scale factor for the pair of similar figures. Explain how she can
determine the scale factor from the figure on the left to the figure on the right.
First, she must identify the Q congruent
equivalent
corresponding
identical
matching
U sides.
Because one side of length12 cm corresponds
to a side of length Q
12 cm
6 cm
3 cm
U , she divides 12 by Q
12
6
3
U .
The result shows that the scale factor is Q 4 3
2
1 __ 2
U .
6 cm
12 cm
3 cm
6 cm
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Investigation 4
Name ____________________________________________ Date ____________ Class ____________
Skill: Similarity and RatiosStretching and Shrinking
Tell whether each pair of polygons is similar. Explain why or why not.
1. 2.
3. 4.
5. 6. P
O
R
Q
T
S
V
U6
64
4
8
8
3
3
4
44
4
H I
JG
9
9
9
9
L M
NK
B
A C
223
F
D E
6 6 9 9
4
9
8
11
T
S U
3
2 23
3 23
W
XV
33
3 4
3
J K
L
M
I
5
5
5
5
8
N
O P
Q
R
CB
A D
12
8
H
G
E
F 4
6
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d.Investigation 4
Name ____________________________________________ Date ____________ Class ____________
Skill: Similarity and Ratios (continued)
Stretching and Shrinking
Exercise 7–11 show pairs of similar polygons. Find the missing side lengths.
7. 8.
9. 10.
11.x
y
12
1627
15
912
18
15
15
30
y
xy
x
30
4215
12
18
x
36 36
12
12
24 yx
y12
74
6
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