Geometry Spring Final Exam Review 1. Find the sum of the measures of the interior angles of a convex hexagon. 2. Find the value of x. 68 ° 110 °
135°
x°
3. Find the values of x and y in the parallelogram when D
C
,
,m
°, m
A
B
4. A parallelogram is formed by the supports that attach a basketball backboard and rim to the wall. The angles change as the basketball apparatus is taken out and put away. Find when .
5. Find the coordinates of the intersection of the diagonals of ,
, and
.
with vertices
,
.
6. For what values of x and y is quadrilateral ABCD a parallelogram?
A
4y+20
8x–34 B
D
6x–4
9x–40 C
7. Find the measures of the numbered angles in rhombus QRST. R
S 4
60° 5
3
1
2
Q
T
8. Find AB. D
M A
16
27
B N C
9. Decide whether quadrilateral
with vertices
,
rhombus, square, or parallelogram. y
:C
4
B
–4
2
–2
2
4
D
x
–2
A–4
10. Quadrilateral ABCD is a kite. What conditions must be true?
,
, and
is a rectangle,
11. In rectangle ABCD,
,
A
, and
. Find the value of y.
B
P D
C
12. The badge shown is shaped like a regular nonagon. Find the measure of each interior angle of the badge. Then find the measure of each exterior angle.
13. Classify the special quadrilateral.
14. The cross section of a brilliant cut diamond is shown. Find the measures of
and
15. Find the number of sides a regular polygon must have so each interior angle measure is 162°. Justify your answer. 16. The triangles are similar. Find the value of x. B R 24 24
30
S 32
C
x
A
T
40
17.
. Find the length of altitude
.
A D 15 E
12
M
N 5 C
B
18. You are going to build a new garage similar to the rectangular one you currently have. The current dimensions are 25 feet wide by 20 feet long. You need to stake and rope off where the concrete will be poured. If the new garage is going to have a width of 30 feet, how much rope are you going to need?
19.
. The area of
is given. Find the area of
.
E
60 B 12 A
C
D
F A = 1200 sq in.
20. A lumber mill needs one more tree cut down that is at least 29 feet long. The person cutting down the tree is 6 feet 2 inches tall. Using shadows to determine whether a tree is tall enough, the person stands next to the tree and measures the length of his shadow as 32 inches. What is the length (to the nearest tenth of a foot) of the tree’s shadow that will allow the tree to be cut down? 21. Find the value of x.
22
x 21
11
22. State a similarity statement(s). P
F
T 82°
I
82° B
M
23. Find the value of x that makes
. T
B 36 2x + 6
48
40 R 25
A
x + 18
S
C
24. You are checking your friend’s work on this problem. Is the solution correct? If not, explain and correct the error. What value of x makes
? Explain. B
40
30
6x + 6 A
Because
32
D
18
C
,
25. An architect is designing a covered bridge to be placed over a ravine. In the diagram, and represent the sides of the ravine, represents the road surface of the bridge, and represents the roof covering the bridge. Would these measurements ensure the roof is parallel to the road surface of the bridge? Explain A
C 10 ft
14 ft F
G
35 ft
30 ft
B
26. An adventure company wants to run a zip line from the top of one building that is 130 feet tall to the top of another building that is 30 feet tall. The two buildings are 72 feet apart. Estimate the length (in feet) of the zip line. Round your answer to the nearest tenth.
27. In the diagram,
28. In the diagram,
2 and
2 . Find AB. Write your answer in simplest form.
. Find AB and AC . Write your answers in simplest form. °
°
29. Gym members are instructed to lift their legs at a 30° angle during leg lifts. One member has legs that are 33 inches long. What is the height (in inches) of the member’s feet during the leg lift? If necessary, round decimal answers to the nearest tenth.
30. Solar panels installed in a backyard have a cross section that is a right triangle. The diagram shows the approximate dimensions of this cross section. A vertical support from the right angle to the ground is recommended. Approximate the length of the support to the nearest tenth of a foot.
13.6 ft
4.4 ft
14.3 ft
31. Find the geometric mean of 12 and 48.
32. Find the value(s) of the variable(s). If necessary, round decimal answers to the nearest tenth.
32
57 °
x
y
33. Find the exact value of the variable
y 16 12
34. A car is traveling along a road that makes a 10° angle with the ground. Find the elevation of the car on a stretch of road that extends horizontally 86 meters. Round your answer to the nearest tenth.
10° 86 m Not drawn to scale
35. A parasailer is attached to a boat with a rope. While parasailing, the angle of depression to the boat is 25°. When the parasailer is attached to the boat with a 300-foot rope, how high above the boat is he? Round your answer to the nearest tenth of a foot. 36. Solve the triangle. Round decimal answers to the nearest tenth.
18
C 29
B 35
A
37. Identify the similar triangles.
Match the statement below with the set of segment lengths it describes. Use each set of segment lengths only once. a. 10, 7, 658 d. 6, 5, 119 b. 6, 6, 38 e. 7, 24, 25 c. 6, 7, 85
38. The segment lengths form a right triangle. 39. The segment lengths form an acute triangle. 40. The segment lengths form an obtuse triangle. 41. The segment lengths do not form a triangle. 42. The segment lengths form a Pythagorean triple.
43. In the diagram, each side of quadrilateral when , , , and E
D
is tangent to .
. Find the perimeter of the quadrilateral
C
J
F
H B G
A
44. Match the value of x. .
C x
5
A
4
B
45. In the diagram,
,
, and
. Find the measure of each arc.
S
a.
U Q
b.
N
c. W
is a diameter of
46. In the diagram,
and
K P
M
J
N H
. Find HP.
47. In the diagram,
and
. Find
.
S
Q R
. Find
48. In the diagram,
.
G
E H F
49. In the diagram, line m is tangent to the circle and
. Find
.
C
A
m B
E
50. Find the value of x. B A (2x + 21)°
G
(5x – 8)°
(4x + 74)°
D C
51. In the diagram,
, J
N M
K
L
,
, and
. Find the value of x.
52. A park downtown has a circular fountain with a walkway that runs tangent to the fountain. You want to find the radius of the fountain using indirect measurement. You stand on the walkway at a point 16 meters from where it meets the fountain. This point is represented by C in the diagram below and is 9 meters from the edge of the fountain. Knowing is tangent to the circle, find the radius r of the fountain.
9m
E
C
r
r
D
16 m
B
53. Find the center and radius of the circle.
R Q
P V
Use the diagram of circle Q to answer the questions. 54. What word best describes
?
55. What word best describes
?
56. Find the diameter of
if
T
measures 31° and the arc length of
R 9 cm
31° P
U
Q
S
S
is 9 centimeters.
57. Convert 186° to radians. 58. Find the area of the kite.
6 cm 11 cm
1 cm
59. Find the volume of the prism.
4m
3m
4m 11 m
60. Pyramid C and Pyramid D are similar. The volume of Pyramid C is 141 square centimeters. Find the volume of Pyramid D.
32 cm 8 cm
Pyramid C
Pyramid D
61. Find the surface area of the cone.
9 cm
4 cm
62. Find the volume of the composite solid.
8m
7m 6m
63. A snowball has a radius of 7 centimeters. What is the volume?
7 cm
64. In the diagram, ABC is a regular triangle inscribed in
. Find the area of triangle ABC given DM=5.
B
D
A
C
M
65. Find the areas of sectors formed by
?
A C 4.1 cm 86.4°
B
66. The diagram shows a block of processed cheddar cheese that has a mass of 227 grams. Find the density of processed cheddar cheese to the nearest hundredth of a gram per cubic centimeter.
67. The m
is 10 centimeters. Find the circumference of
A
B 114º 10 cm
C
.