Download Geometry Chapter 7 Study Guide Answer Section

Geometry
Chapter 7 Study Guide
1. What is the value of x?
>
24
36
x
>
12
>
2. Figure
. What are the pairs of congruent angles?
3. In a diagram of a landscape plan, the scale is 1 cm = 10 ft. In the diagram, the trees are 4.6 centimeters apart.
How far apart should the actual trees be planted?
Find the geometric mean of the pair of numbers.
4. 32 and 8
5. 5 and 9
6. What is the value of x?
x–2
x
x+5
>
x+1
>
7. Jason wants to walk the shortest distance to get from the parking lot to the beach.
Refreshment
Stand
40 m
Beach
Parking
Lot
30 m
a.
b.
8.
How far is the spot on the beach from the parking lot?
How far will his place on the beach be from the refreshment stand?
Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale.
6
18
What are the values of a and b?
9.
)
100
a
4
)
b
10. What is the value of x to the nearest tenth?
5.6
x
))
))
5.5
12.1
Not drawn to scale.
11. The measures of the angles of a triangle are in the extended ratio 5 : 6 : 7. What is the measure of the smallest
angle?
12. 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.
Are the polygons similar? If they are, write a similarity statement and give the scale factor.
S
V
10
12
T
R
32º
15
32º
W
U
18
Not drawn to scale.
13.
14. What is the value of x, given that
A
9
P
45
B
x
Q
25
C
What is the solution of each proportion?
?
15.
16.
17.
bisects
, LM = 18, NO = 4, and LN = 10. What is the value of x?
N
O
x
L
M
18. Are the two triangles similar? How do you know?
J
H
47 °
M
47 º
K
G
State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem
you used.
V
8
Q
16
U
T
32
29º
S
64
19.
R
29º
20.
B
O
5
M
12
5
7.5
8
A
7.5
C
N
21.
O
J
36
12
M
21
K
7
N
The polygons are similar, but not necessarily drawn to scale. Find the value of x.
22.
23. The measure of two complementary angles are in the ratio 1 : 4. What are the degree measures of the two
angles?
24. A model is made of a car. The car is 2 meters long and the model is 4 centimeters long. What is the ratio of
the length of the car to the length of the model?
Geometry
Answer Section
Chapter 7 Study Guide
1. 8
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
46 feet
16
3 5
5
24 m; 32 m
6 3
a = 20, b = 4
12.3
50
20 ft
13.
26
;
14. 5
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
7
7.2
yes, by AA
; SAS
; SSS
; SAS
x=9
18° and 72°
50 : 1