### Unit 5

```Unit 5
review
QUESTION 1
A transformation where a geometric figure is
reduced or enlarged in the coordinate
plane is called a
_____________________
Dilation
QUESTION 2
Figures that are exactly the same size and
the same shape are ________________
figures.
congruent
QUESTION 3
List the characteristics of similar figures.
*same shape
*corresponding angles are congruent
*corresponding sides are proportional
QUESTION 4
One vertex of a triangle on the coordinate
plane has the ordered pair of (32, 16).
The rectangle undergoes a ¼ dilation.
What would be the new coordinates of
the corresponding vertex?
(8, 4)
Question 5
•
Cheryl wants to dilate a photograph that
has a width of 17.5 inches and a length
of 24.5 inches to fit into a frame that is 7
inches in length. What will be the width
of the new photograph?
5 inches
You can set up a proportion. Or, you can
divide 24.5 by 7, which equals 3.5. Then,
divide 17.5 by 3.5.
Question 6
•
Stacey decides to dilate the area of her
rectangular garden. The length of her
original garden is 10 feet and the area is
45 square feet. The length of the new
garden will be 15 feet. What is the area
of the new garden?
101.25 ft²
A = 45 ft²
4.5 ft
10 ft
Scale Factor = 1.5
Area Scale Factor = 2.25
A = 101.25 ft²
15 ft
6.75 ft
Question 7
Find the value of x if triangle ABC ~ triangle
JPH
A
J
x
15
H
12
C
66
B
P
• X = 82.5
Question 8
• Determine the scale factor of the first
figure to the second figure.
7 in
11 in
11/ 7 in
Question 9
State whether the dilation would be
reduced, enlarged, or congruent.
Scale factor = 1/17
reduced
Question 10
State whether the dilation would be reduced,
enlarged, or congruent.
Scale factor = 17
enlarged
Question 11
• A vertex of a rectangle on the coordinate
plane is (-4, -2). The rectangle is dilated
and the new coordinate of the vertex is
(-2, -1). What was the scale factor of the
dilation?
1/2
Question 12
State whether the dilation would be reduced,
enlarged, or congruent.
Scale factor = 1
congruent
Question 13
If triangle ABC ~ triangle JPH. Which
proportion can be used to find the value of x?
A
J
x
15
H
12
C
66
B
P
Question 14
Determine the scale factor from the
reduction of the first figure to the second
figure.
3
5
3
5
Question 15
Find the area of the smaller similar rectangle.
8
x
4
16
Area = 8
*scale factor is 4/16 or ¼. 8 times ¼ = 2.
Therefore, x = 2.
Area = length times width
8=2•4
Question 16
Find the area of the larger similar rectangle.
x
5
4
14
Area = 245
14 ÷ 4 = 3.5
x = 5 • 3.5
x = 17.5
17.5 • 14 = 245
Question 17
If rectangle ABCD ~ rectangle WXYZ, what
side corresponds with YZ?
CD
Question 18
Rectangle ABCD ~ rectangle WXYZ.
Is WX congruent to BC?
No
Question 19
Are all squares similar?
Yes
Question 20
A flagpole is 28 ft tall and has a shadow of
20 ft. How tall is a nearby tree if its
shadow is 30 ft?
42 feet
Question 21
Triangle ABC ~ to triangle WXY. Use the
diagram to find the perimeter of triangle
ABC.
A
W
5m
4m
X
3m
B
21 m
C
Y
The area of the large triangle is 84 m.
*3 • 7 = 21 Therefore, the scale factor is 7.
4 • 7 = 28 and 5 • 7 = 35.
Add the sides of the large triangle to get the
perimeter. 28 + 35 + 21 = 84 m.
Question 22
21 in
x in
12 in
7 in
x = 4 in
Question 23
One vertex of a triangle on the coordinate
plane has the ordered pair of (24, 16). The
triangle undergoes 1/8 dilation. What
would be the new coordinates of the
corresponding vertex?
(3, 2)
Question 24
• Brooke is 5 ft tall. She and her class are
walking through a wooded area looking for
a tree that is 50 ft. tall. If the length of
Brooke’s shadow is 2 ft, how will the
students know when they have found a 50
ft tree?
• When they find a tree’s shadow that
measures 20 feet.
Question 25
• A shrub is 1.5 meters tall and casts a
shadow 3.5 meters long. At the same time,
a radio tower casts a shadow 98 meters
long. How tall is the radio tower?
42 meters
Question 26
Linda wants to enlarge a 5 inch by 7 inch
photograph that will fit into a frame that is
21 inches long. What is the width of the
new photograph?