Name: ___________________________
Chapter 8 Test – Comparing
100 points
SHOW YOUR WORK\PROVE YOUR ANSWERS!!!
Figures not drawn to scale unless noted
Just because a question looks similar, don’t assume it’s the same as on the quizzes… read
Each question is 5 points
1. Two ratios that are equal are called a __________________________________.
2:
Give a loose definition of what makes shapes similar or congruent.
What is the symbol for similar?
3. For two polygons to be similar, what must be true about the parts of the polygons?
4:
A comparison between two values of different types, such as 28 pounds/gallon
is called a _____________________________.
What is a scale factor?
5. For each statement below, is the statement valid or invalid, given
?
ad = bc
6:
In a dilation, what value of k will give you an exact copy of the original shape with the same size?
Simplify this ratio:
Pick one: ABCDE and VWXYZ are [definitely similar, maybe similar, or not similar]. Must
show\explain why or why not fully?
C
Y
2
4
X
4
B
6
5
A
D
2
W
3
4
10
Z
2
V
E
7:
Write the ratio of planets that start with an M to planets that start with a V.
What is the ratio of planets that start with a vowel to planets that start with a consonant
(write out the planets or no points if you get the question wrong).
8. In a park, there are 16 geese to every 9 ducks. How many geese are in the park if there are 144
geese?
9. I can drive 300 miles in 4 hours. How far can I get in 50 minutes?
10. It costs $0.15 for each 1/8 of a mile in a taxi. How many miles did you ride if you paid $9.00?
11. The sides of the rectangles MNOP and QRST are proportional. What is the value of x? Show work.
M
P
Q
T
8
N
x
20
O
R
32
S
12. Pentagon ABCDE is similar to pentagon FGHIJ. Solve for z. Show work.
A
4
F
6
E
97°
12
B
100°
z
J
G
8
14
95°
C
D
I
95°
110°
9
H
13. Determine the value of x in the shape below. Show your reasoning, including why you are able to
make any conclusions you need to.
4
x
5
6
17
14. Determine the value of x below. Show your reasoning, including why you are able to make any
conclusions you need to.
H
J
30
4
10
T
N
20
x
I
O
15. Determine the measure of angle C in the shape below. Include all reasoning.
A
B
9
X
5
W
15
21
96°
3
93°
89°
4
82°
C
D
12
Z
16. You are given the ratio of sides in a triangle. Which two are similar?
a) 4 – 9 – 11
b) 8 – 11 – 15
c) 12 – 16 – 20
d) 21 – 33 – 39
e) 21 – 28 – 35
f) 24 – 29 – 45
17. Blow up the figure below using a scale factor of 4 and point H.
H
B
P
L
I
7
Y
18. Dilate the figure below using a scale factor of 1/2 and point C.
C
19. At 12:15 PM, you see that the shadow of the Empire State Building is 55 feet long. You are 6 feet
tall, and your shadow is ¼ of a foot. Determine the height of the building.
Question 20: Use the simplified diagram of the eye below and the proportion 25/r = d/h.
25 mm
d
r
h
Lens
20:
An object that is 50 meters away appears on the retina as 2 mm tall. How tall is the object?
An object that is 1 meter tall appears on the retina as 1 mm tall. How far away is the object?
Extra Credit:
1. Solve for the value of x. Show all work!
[8 points]
16
9
x-4
2. If at a foreign market, you saw that 2 pounds of turkey cost 11 Euro,
based upon the table, how much would 12 ounces cost in Rubles?
[3 points]
3. Mary, who is sixteen years old, is four times as old as her brother. How old will Mary be when she is
twice as old as her brother? [2 points]
4. If all Bloops are Razzies and all Razzies are Lazzies, then all Bloops are definitely Lazzies? Is this true
or false? Why? [2 points]
5. ΔEGO is similar to ΔERA. Prove that GO and RA are parallel in the triangles below.
E
G
R
[8 points]
O
A
6. When a shape gets bigger due to a dilation, it is called a\an _____________________________.
[2 points]
7. When a shape gets smaller due to a dilation, it is called a\an ____________________________.
[2 points]
8. Determine the values of all sides and angles in the figure below.
Explain all your work!!! [8 points]
[May be best to label steps and provide reasoning below the figure.]
A
5
D
F
J
15
C
18
60°
I
12
E
4
K
G
B
∠GFI ≅ ∠GHI
∠GHI = 35°
HIJKLM is a regular hexagon
∠FIH = 145°
∠EGH = 160°
C is the midpoint of AG
AB = 16
H
L
M