L2 Geo Pract Ch 7 Test
1. Are the two triangles similar? How do you know?
J
H
M
39 °
39 º
K
G
State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem
you used.
O
M
12
B
5
7.5
5
8
A
C
N
2.
O
J
33
21
K
7
N
3.
7.5
11
M
V
8
Q
16
U
T
32
29º
S
29º
R
64
4.
5. What is the value of x?
x
x+5
x–2
>
x+1
>
Find the geometric mean of the pair of numbers.
6. 81 and 4
7. 4 and 7
The polygons are similar, but not necessarily drawn to scale. Find the value of x.
x –3
8
2
2.5
4
16
8.
A
D
5x
5
E x F
B
9.
4
C
____ 10. The two rectangles are similar. Which is the correct proportion for corresponding sides?
4m
8m
12 m
24 m
A.
B.
11. What is the value of x, given that
C.
?
D.
A
x
7
P
Q
35
40
B
C
12. Use the information in the diagram to determine the height of the tree to the nearest foot.
13. What is the value of x?
>
3x
4x
3x + 7
>
>
5x – 8
Are the polygons similar? If they are, write a similarity statement and give the scale factor.
14. In QRS, QR = 4, RS = 15, and mR = 36. In UVT, VT = 8, TU = 32, and mT = 36.
A
10
N
B
5
5
1.2
K
3.12
3.12
D
10
C
M
1.2
L
Not drawn to scale.
15.
What is the solution of each proportion?
16.
17.
18.
Which theorem or postulate proves the two triangles are similar?
10
20
>
5
>
19.
Not drawn to scale.
20. What is the value of x to the nearest tenth?
4.6
x
5.1
12.2
Not drawn to scale.
21. In a diagram of a landscape plan, the scale is 1 cm = 10 ft. In the diagram, the trees are 3.1 centimeters apart.
How far apart should the actual trees be planted?
22.
bisects
, LM = 18, NO = 4, and LN = 10. What is the value of x?
N
O
x
L
____ 23. If
A.
M
, then = ____.
B.
C.
24. Are the two triangles similar? How do you know?
D.
D
53°
G
60°
C
60°
E
F
67°
H
25.
The Sears Tower in Chicago is 1450 feet high. A model of the tower is 24 inches tall. What is
the ratio of the height of the model to the height of the actual Sears Tower?
L2 Geo Pract Ch 7 Test
Answer Section
1. yes, by AA
2.
3.
4.
5. 5
6. 18
7.
8.
9.
10.
11.
12.
; SSS
; SAS
; SAS
2 7
x = 13
2
B
8
80 ft
13.
14. The triangles are not similar.
15. The polygons are not similar.
16. –3
17.
18.
19.
20.
21.
22.
23.
24.
25.
8
AA Postulate
11
31 feet
7.2
C
yes, by AA
1 : 725