Download Unit 5 – Similarity TEST

Name: __________________________________________ Date: ___________________________
Unit 3 – Similarity Review
Multiple Choice
1]
In the diagram below ABC , D is a point on AB , E is a point on CB , DE is drawn,
and BAC  BED.
A
Which reason justifies the conclusion that ABC ~ BED ?
(1) ASA
(3) SAS
(2) AA
(4) SSS
D
C
2]
The following two triangles are similar.
 Find the scale factor of the sides.
x
 Find the altitude.
B
E
12
12
16
 Find the perimeter of each triangle. Now find the ratio of the perimeters.
 Find the area of each triangle. Now find the ratio of the areas.
 What do you notice about the scale factors for the sides, perimeter & area?
 The corresponding angles in similar triangles are: _____________.
3]
The accompanying diagram shows two similar triangles
34
26
x
25
9
17
Which proportion could be used to solve for x?
(1)
25 9

17 x
(2)
x 25

9 17
(3)
x 26

9 34
(4)
34 9

x 26
4]
Given: AE || BD. Find the length of AB .
5]
A builder is building a rectangular playground with dimensions of 10 feet by 24 feet.
To ensure that the sides form 90o angles, what should each diagonal measure?
(1) 26 ft
(2) 34 ft
(3) 46 ft
(4) 30 ft
6]
Which equation could be used to find the length of x.
(1) 122 + x2 = 162
(2)
12
x

x 28
(3) 122 + x2 = 282
(4)
12 x

x 16
7]
In a 450–450–900 triangle, the hypotenuse is
(2) 2
(1) 3
8]
In a 300-600-900 triangle, the hypotenuse is
(1) 2
(2) 2
9]
In a 300-600-900 triangle, the longer leg is
(1) 4
(2) 3
28
ft
16 ft
?
times as long as each leg?
3
2
(4)
(3)
2
2
?
?
times as long as the shorter leg?
(4) 3
(3) 3
times as long as the shorter leg?
(4)
(3) 3
2
10]
The measures of the angles in ABC are in the extended ratio of 2:7:9. What is the
measure of the smallest angle?
(1) 700
(2) 200
(3) 150
(4) 170
11]
Find the geometric mean of the following two numbers: 9 and 8
(1) 72
(2) 12 2
(3) 6 2
(4) 9 8
Part II Questions
12]
At the same time of day, a man who is 52.8 inches tall casts a 68.8 inch shadow and his
son casts a 43-inch shadow. What is the height of the man’s son?
13]
Find the values of x and y in the following diagram.
600
X
8 3
Y
300
14]
Using a compass and a straightedge, construct a line that passes through point P and is
perpendicular to line m. [Leave all construction marks.]
B
15]
Given  ABC with segments BD , BE , DA , EC . Is DE is parallel to AC ? 9
Explain why or why not.
D
15
E
24
12
C
A
16]
Part III Questions
In the diagram below of right triangle ACB, altitude CD intersects AB at D. If AD = 5
and DB = 8, find the length of CD in simplest radical form.
5
8
17]
In  DEF, DE = 8, EF = 15, and m  E = 37. In  GHI, HI = 16, IG = 32, and
m  I = 37. Sketch a diagram of the two triangles and state whether the triangles are
similar. If they are similar, write a similarity statement.
Part IV Questions
18]
Find the value of q, x, y, and z in the following diagram.
x
y
7 3
300
z
q
600