Geometry R
U5L9-10 Review Packet
Name _____________________________
1. The geometric mean of 4 and 16 is:
2. The geometric mean of 8 and 18 is:
3. The geometric mean of 10 and 40 is:
4. The geometric mean of 24 and 150 is:
5. If g is the geometric mean of a and b then which of the following is NOT true?
A)
a
b

g
g
B)
g
b

a
g
C) ab  g 2
D)
a
g

g
b
6. If h is the geometric mean of m and n then which of the following is NOT true?
A)
h n

m h
B) h 
mn
h
D) hm  hn
C) mn  h2
B
7. Which statement is NOT true?
A) ADB  BDC
C) ABC  ADB
B) 2(ADB)  BDC
D) ABD  BCD
o
A
x
D
C
8. Find the missing values. (Leave answers as a whole number, reduced fraction, or in simplest radical
form)
a)
b)
x
z
y
x
4
12
c)
5
z
y
3
12
z
y
x
3
9. Find the missing values. (Leave answers as a whole number, reduced fraction, or in simplest radical
form)
a)
b)
c)
4
z
12
y
x
6
x
9
z
5
y
z
y
4
x
10. Find the missing values. (Leave answers as a whole number, reduced fraction, or in simplest radical
form)
a)
b)
x
12
y
c)
x
8
z
y
x
8
8
y
z
11. Find the missing values. (If not a whole number, leave it in simplest radical form)
a)
b)
x+2
5
x
x+3
x
z
8
12
9
12. Solve for the unknowns.
(E) = leave your answer in exact form (without rounding) - in some cases that will be a reduced radical.
a)
b)
c)
d)
o
x
12 3
60°
x
x
15
x = __________ (E)
x = __________ (E)
y = __________ (E)
e)
o
15
x
o
y
60°
y
10
6
60°
y
x = __________ (E)
y = __________
x = __________
(E)
f)
g)
h)
x
6 2
6 3
o
60°
x
y
o
y = __________ (E)
2 3
x
60°
o
y
x
x = __________ (E)
x = __________
x = __________
y = __________
x = __________
y = __________ (E)
13. Solve for the unknowns.
(E) = leave your answer in exact form (without rounding) - in some cases that will be a reduced radical.
a)
b)
c)
d)
20 3
x
30°
y
o
o
16 10
x
x
x = __________
y = __________
8 7
o
2.5
x = __________ (E)
o
x = __________ (E)
30°
y
x = __________ (E)
y = __________ (E)
x
e)
f)
\g)
x
y
30°
h)
x
9 2
15
o
4 6
y
30°
x
x
21
y
30°
o
x = __________ (E)
x = __________
x = __________
y = __________ (E)
y = __________ (E)
x = __________ (E)
y = __________ (E)
14. Solve for the unknowns.
(E) = leave your answer in exact form (without rounding) - in some cases that will be a reduced radical.
a)
b)
c)
x
9 2
o
30°
x = __________
x
x
o
8
y
o
d)
8 14
y
o
x = __________ (E)
x = __________ (E)
y = __________
e)
x = __________ (E)
y = __________
f)
g)
h)
y
y
y
x
30°
18 3
30°
10 3
x
30°
x
24 2
x = __________
x = __________ (E)
y = __________
y = __________ (E)
14 5
o
o
x
x = __________ (E)
30°
6
x = __________ (E)
y = __________ (E)
x
15. If the area of a right isosceles triangle is 8 cm2, then the length of the hypotenuse is:
A) 4 cm
B) 4 2 cm
C) 8 cm
D) 8 2 cm
16. If the area of a right isosceles triangle is 18 cm2, then the length of one of the legs is:
A) 6 cm
B) 6 2 cm
C) 9 cm
D) 18 cm
17. What is the area of a square that has a diagonal length of 12 2 cm?
18. What is the area of a square that has a diagonal length of 12 cm?
19. If the long leg of a 30,60,90 triangle is 6 3 cm, then the area of the triangle is:
A) 54 cm2
B) 9 3 cm2
C) 18 cm2
D) 18 3 cm2
20. If the long leg of a 30,60,90 triangle is 12 cm, then the area of the triangle is:
A) 24 3 cm2
B) 48 3 cm2
C) 72 3 cm2
D) 72 cm2
21. If the short leg of a 30,60,90 triangle is 12 cm, then the area of the triangle is:
A) 24 3 cm2
B) 48 3 cm2
C) 72 3 cm2
D) 72 cm2
22. If the hypotenuse of a 30,60,90 triangle is 12 cm, then the area of the triangle is:
A) 18 3 cm2
B) 36 3 cm2
C) 36 cm2
D) 72 3 cm2
23. Determine the area of the given shapes.
a)
Area =
______________
b)
Area =
______________
12 cm
8 cm
24. Determine the area of the given shapes.
a)
Area =
______________
b)
Area =
______________
12 cm
8 cm