Download Geometry: Chapter 7 Study Guide

Geometry: Chapter 7 Study Guide
1. The measure of two complementary angles are in the ratio 1 : 5. What are the degree measures of the two
angles?
2. The ratio of length to width in a rectangle is 3 to 1. If the perimeter of the rectangle is 136 feet, what is the
length of the rectangle?
3. The measures of the angles of a triangle are in the extended ratio 2 : 3 : 4. What is the measure of the smallest
angle?
What is the solution of each proportion?
4.
5.
6. Figure
. What are ALL the pairs of congruent angles?
Are the polygons similar? If they are, write a similarity statement and give the scale factor.
S
V
10
12
T
15
32º
W
U
18
Not drawn to scale.
7.
R
32º
A
10
N
B
1.2
K
5
5
3.12
3.12
D
M
C
10
1.2
L
Not drawn to scale.
8.
The polygons are similar, but not necessarily drawn to scale. Find the value of x.
x –3
8
2
2.5
4
16
9.
A
D
5x
5
E x F
B
10.
4
C
K
B
J
A
L
C
8
4
55
x
D
11.
M
12. Are the triangles similar? How do you know?
30.4°
84.6°
84.6°
66°
13. 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.
14.
15.
O
33
J
21
K
7
N
11
M
V
8
Q
16
U
T
32
29º
29º
S
R
64
16.
Which theorem or postulate proves the two triangles are similar?
17.
10
20
>
5
>
Not drawn to scale.
18.
)
76/5
16
)
20
19
Not drawn to scale.
19. Use the information in the diagram to determine the height of the tree to the nearest foot.
20. Michele wanted to measure the height of her school’s flagpole. She placed a mirror on the ground 48 feet
from the flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her eyes
were 5 feet above the ground and she was 12 feet from the mirror. Using similar triangles, find the height of
the flagpole to the nearest tenth of a foot.
Find the geometric mean of the pair of numbers.
21. 242 and 8
22. 81 and 4
23.
Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale.
7
18
24. What is the value of x, given that
?
A
8
P
x
B
12
Q
18
C
25. What is the value of x, given that
?
A
x
7
P
Q
35
40
B
C
26. What is the value of x, given that
?
A
x
B
11
E 5 D
7
C
27. What is value of x, given that
?
O
P
9
N
x
Q
18
20
M
28. What is the value of x?
>
29.
24
36
x
>
12
>
bisects
, LM = 18, NO = 4, and LN = 10. What is the value of x?
N
O
x
L
M
30. What is the value of x to the nearest tenth?
4.6
x
))
))
5.1
12.2
Not drawn to scale.