Name:
Class:
7th Grade PreAP
Date:
Unit 4 Review: Similarity and Dilations
Use notebook paper to show work for all questions. Staple it to this review sheet!
1. Triangle JKL has vertices J(0, 2), K( 1, 2) and L(0, 3).
The triangle is dilated with a scale factor of 4, and the dilation
will be centered at the origin. Determine the coordinates of the
image of point K after the dilation.
7. A 15-foot-tall pole casts a shadow that is 6 feet long.
Nearby, a tree casts a shadow that is 4 feet long. How tall is
the tree?
8. On a map, two cities are
2. On the graph below, segment M'N' is a dilation of segment
MN. What is the scale factor of the dilation?
map is
inches a part. The scale of the
inch 2 miles. What is the actual distance between
the two cities?
For problems 9 and 10, determine whether the triangles
are similar by angle-angle similarity. If so, write a
similarity statement.
9.
3. A rectangle is 5 feet long and 2 feet wide. A rectangle
similar to the first rectangle has a width of 8 feet. What is the
length of the second rectangle?
a. no
b. yes;
4. Rectangle DEFG is similar to rectangle JKLM. Rectangle
DEFG has a length of 5 units and a perimeter of 16 units.
Rectangle JKLM has a length of 10 units. What is the
perimeter of rectangle JKLM?
5.
and
, so
c. not enough information given
d. yes;
and
, so
. Find the missing side.
10.
6. The figures are similar. Determine the missing side.
a. yes;
and
so
b. yes;
and
so
c. no
d. not enough information given
11. Carol draws rectangle ABCD, which has an area of 25
square units. Sam draws a similar rectangle whose side lengths
are twice as long as the side lengths of rectangle ABCD. What
is the area of the rectangle that Sam drew?
17. Louise has a television in her family room that is 3 feet
wide and 5 feet long. She has a television that is similar in
shape in her bedroom that is 1.5 feet long. What is the
perimeter of the television in Louise’s bedroom?
12. The scale factor of a model car from the actual car is 24:1.
If one of the tires of the model car has a diameter of
inch,
what is the length of the diameter of the tire on the actual car?
18. Christina is building a diorama of the ocean. The table
shows the lengths of different ocean animals. The scale of the
diorama is 1 inch 2 feet. How long is the actual shark, in
feet?
13. A 40-foot-tall flagpole casts a shadow that is 8 feet long.
Find the length, in feet, of a shadow cast by a nearby man who
is 6 feet tall.
14. Polygon ABCD has vertices A(5, -2), B(3, -2), C(3, 3), and
D(5, 3). Polygon ABCD is dilated using the origin as the
center of the dilation. The image is polygon A'B'C'D', and A’
has coordinates (10, -4). Find the area of polygon
A'B'C'D'. Use a problem-solving model to solve.
19. Rectangle ABCD has vertices A( 1, 2), B(4, 2), C( 4, 1),
and D( 1, 1). Rectangle ABCD is
dilated by a scale factor of
. Which statement is true?
a. Rectangle ABCD and rectangle A'B'C'D' are
congruent.
b. Rectangle ABCD and rectangle A'B'C'D' are
similar. Rectangle ABCD is larger than
rectangle A'B'C'D'.
c. Rectangle ABCD and rectangle A'B'C'D' are
similar. Rectangle ABCD is smaller than
rectangle A'B'C'D'.
d. Rectangle ABCD and rectangle A'B'C'D' are
similar. Rectangle ABCD is the same size as
rectangle A'B'C'D'.
15. The map of a park shows that a pond is 4 inches away
from a playground. The scale of the map is 1 inch represents
5.25 meters. How far apart are the actual pond and
playground?
Determine whether the polygons are similar.
16. A diagram of a lot of land is shown. The scale on the
diagram is 1 centimeter represents 2.5 yards. What is the area
of the actual lot of land?
a. 44 sq yd
c. 110 sq yd
b. 105 sq yd
d. 656.25 sq yd
20.
a. not similar
c. not enough information given
b. similar
d. none of these
Page 2
Answer Key
K’( 4, 8)
1.
2. 2
3. 20 ft
4. 32 units
1
5. 9 in
3
6. 8 cm
7. 10 ft
8. 18 mi
9. b
10. c
11. 100 𝑢𝑛𝑖𝑡𝑠 2
12. 18 in
13. 1.2 ft
14. 40 𝑢𝑛𝑖𝑡𝑠 2
15. 21 m
16. d
17. 4.8 ft
18. 8
19. b
20. a
Page 3
Answer Key
1.
K’( 4, 8)
2. 2
3. 20 ft
4. 32 units
1
5. 9 in
3
6. 8 cm
7. 10 ft
8. 18 mi
9. b
10. c
Page 4