Geometry Exam Review—These problems are required and are due the day of your exam. They

will be worth 10% of your final exam grade. Answers will be posted on the website. You will be

provided with the attached formula sheet for your exam. Answers and necessary work must be

done neatly on a separate sheet of paper. Messy work will not be accepted. *indicates work must

be shown.

Chapter 6

*1.Find the measure of each interior angle of a regular 30-gon.

*2.Find the measure of each exterior angle of a regular pentagon.

3.The diagram shows the parallelogram-shaped component that attaches a car’s rearview mirror to the car. In parallelogram

RSTU, UR = 32, RX = 18, and = 38.6. Find ST, RT, and m RST.

*4.MNOP is a parallelogram. Find MP.

5.An artist designs a rectangular quilt piece with different types of ribbon that go from the corner to the center of the quilt.

The dimensions of the rectangle are AB = 20 inches and AC = 34 inches. Find BX.

*6.TRSU is a rhombus. Find .

R

S T

U

X

A

CB

X

D

4y - 4

T U

R S

2y + 12

M N

O P

8x+3 6x+9

*7.In kite PQRS, 40m QPO and 35m QRO . Find m .

8.Given isosceles trapezoid ABCD with , BD = 20 , and AY = 14. Find YC.

*9.QS = x + 6 and RT = 2x - 2 . Find the value of x so that QRST is isosceles.

10.Find RS given that RS = 14 and XY = 18. X and Y are midpoints.

Chapter 7

*11.The ratio of the side lengths of a quadrilateral is 4:2:5:7, and its perimeter is 117 meters. What is the length of the

shortest side?

*12.Solve the proportion .

P

Q

S

RRO

A

B

D

C

Y

Q T

SR

>>

>>

Q T

S R

X Y

>>

>>

*13.Sally designs a rectangular vegetable garden. What will be the width of the full-size vegetable garden?

*14.One equilateral triangle has sides 20 ft long. Another equilateral triangle has sides 25 ft long. Find the ratio of the areas

of the triangles.

15.Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement.

*16.A video game designer is modeling a tower that is 280 ft high and 240 ft wide. She creates a model so that the similarity

ratio of the model to the tower is . What is the height and the width of the model in inches?

*17.To find out how wide a river is, John and Sally mark an X at the spot directly across from a big rock on the other side of

the river. Then they walk in a straight line along the river, perpendicular to the straight line between the X and

the rock. After walking for 20 feet Jon stops while Sally continues along the straight line for another 10 feet.

Then she makes a 90 degree turn and walks for 30 feet. When she stops and looks at the rock she sees that the

straight line from her to the rock passes through John. What is the distance from X to the rock?

*18.Find .

M

P

R

N

Q 3 12

8

Rock X

Jon

Turn Sally

distance

30 ft

18 ft

40 ft

15

20 R S

T U

6

8 M N

O P

Design

Full-size Vegetable Garden

24 in.

36 in.

?

60 in

*19.An artist used perspective to draw guidelines in her picture of a row of parallel buildings. How many centimeters is it

from Point B to Point C?

*20. Find .

*21. A tree is standing next to a 75-foot high building. The tree has a 14-foot shadow, while the building has a 20-foot

shadow. How tall is the tree, rounded to the nearest foot?

*22. A model airplane is built to a scale of 1 in.:9 ft. If the model plane is 8 inches long, find the length of the actual plane,

rounded to the nearest foot.

*23.A house is 36 feet wide and 72 feet long. If a sketch is made of the house using the scale

1 cm: 8 ft, what are the dimensions of the sketch?

*24.Given , find the perimeter and area of .

J

K

L

16

A

B

C

12

P = 28 ft

A = 18 ft 2

A

B

C

4y - 2

24

D

2y

14.4

5 cm

6 cm

3 cm

A

B

C

F

D

H

Chapter 8

*25. Find the geometric mean of the pair of numbers 2 and 50.

26.Write the trigonometric ratio for sin Y, cos Y, and tan Y as a fraction and as a decimal rounded to the nearest hundredth.

*27.Use a special right triangle to write sin 60 and cos 45° as a fraction.

28.Use your calculator to find trigonometric ratios sin 76 , cos 46 , and tan 53 . Round to the nearest hundredth.

*29.Find FH. Round to the nearest hundredth.

*30.Jessie is building a ramp for loading motorcycles onto a trailer. The trailer is 3.1 feet off of the ground. To avoid making

it too difficult to push a motorcycle up the ramp, Jessie decides to make the angle between the ramp and the

ground 12 . To the nearest hundredth of a foot, find the length of the ramp.

31.Use your calculator to find the angle measures to the nearest tenth of a degree.

*32.The coordinates of the vertices of are . Find m Q .

33.Classify each angle in the diagram as an angle of elevation or an angle of depression.

*34.When Rowena stands far away from the pyramid, her line of sight to the top of the pyramid forms an angle of elevation

of 18 with the ground. The horizontal distance between the center of the pyramid and Rowena is 200 feet.

What is the height of the pyramid? Round to the nearest meter.

*35.An eagle 200 feet in the air spots its prey on the ground. The angle of depression to its prey is 16 . What is the

horizontal distance and the actual distance between the eagle and its prey? Round to the nearest foot.

1

23

4

F

G

H 42°

28.4 in.

X

Y

Z 8

10 6

Chapter 10

*36.Find the area of the parallelogram.

*37.Find the area of a trapezoid, in which

*38.Find the area of in terms of .

*39.Find the area of a regular hexagon with side length 10 m. Round to the nearest tenth.

10 in.h

6 in.

12 in.

11 cm

12 cm

5 cm

8 in.

P

5 m

10 m

apothem

*40.Find the area of the composite figure.

*41.Find the shaded area. Round to the nearest tenth.

*42.Find the area of the triangle with vertices (0, 2), (5, 2) and (2, -1).

43.Estimate the area between the graph of and the x-axis.

44.The radius of A is multiplied by . Describe the effect of the change on the area.

45. A point is chosen randomly on . Find the probability that the point is not on BC ?

6 in.

5 in.

A 8 in.

A C B

12 3

11 ft

11 ft

22 ft

15 ft

9 in

15 in

46. Find the probability of the pointer landing on a new car.

Chapter 11—We did not really cover this but you should be fine using the formulas on the formula sheet--

*47.Find the surface area of the right cylinder. Give your answer in terms of .

*48.Find the volume of a right rectangular prism with length 13 in., width 7 in., and height 8 in. Round to the nearest tenth,

if necessary.

*49.Find the volume of the composite figure. Round to the nearest tenth.

*50.Find the volume of a sphere with diameter in.. Give your answer in terms of .

120º60º

New Car

New House

$10,000 New Boat

4 m

8 m

3 cm

10 cm

4 cm

Chapter 12

51.Identify a chord, secant, and tangent that intersects .

*52. and are tangent to . Find .

*53.The circle graph shows the colors of automobiles sold at a car dealership. Find m(arc)EB.

54.Find m(arc)CAB.

A

B

l

D C

A

C

PB

Black 20%

Blue 30%

E

D

Yellow 35%

Red 10%

Green 5%

A

B

C DP

F

50º

A B

C

4x - 1

2x + 9 P

*55. . Find .

*56.Find .

*57.Jenny’s birthday cake is circular and has a 18 cm radius. Her slice creates an arc with a central angle of 60°. What is the

area of Jenny’s slice of cake? Give your answer in terms of . Do you think Jenny will get a stomach ache?

*58.Find the arc length of an arc with measure 140º in a circle with radius 3 in. Round to the nearest tenth.

59.Find .

B

A

B

C

24º

M 3 in

L 140º

A

F

B D C 2

3

W

X

Y

Z

(5y + 5)º

(7y - 43)º

*60.A wheel from a motor has springs arranged as in the figure. Find m .

*61.Solve for x.

62.Find m .

*63.Find m .

A

B

C

D

P 135º

156º

A

C

D

138º

A B

C

(4x + 10)º

O

A B

C

25º

C D

40º O

*64.Find m .

*65.Two of the muscles that control eye movement are attached to the eyeball and intersect behind the eye as shown. If

m(arc)AF = 100°, what is ?

Chapter 6

Matching

Match each vocabulary term with its definition. Each choice can only be used once.

a. rectangle

b. kite

c. square

d. parallelogram

e. rhombus

f. polygon

g. trapezoid

66. a quadrilateral with four right angles

67. a quadrilateral with four congruent sides and four right angles

68. a quadrilateral with four congruent sides

69. a quadrilateral with two pairs of parallel sides

70. a quadrilateral with exactly two pairs of congruent consecutive sides

D

A

F

B

A

C

B

135º 25º

D

Formula Sheet for Semester Exam

Formulas you will need for a convex n-gon.

Sum of the interior angles: 2 180n

Each interior angle (regular polygon): 2 180n

n

Sum of exterior angles: 360

Each exterior angle (regular polygon): 360

n

Area Formulas:

Rectangle A = lw l = length, w = width

Parallelogram A = bh b = base, h = height

TriangleA = ½ bh b = base, h = height

Trapezoid A = ½ h(b1 + b2) h = height, b1,b2 = bases

Rhombus A = ½ d1d2 d1,d2 = diagonals

Kite A = ½ d1d2 d1,d2 = diagonals

Reg. Polygon A = ½ aP a = apothem, P = perimeter

Circle A = πr2 r = radius

C = πd = 2πr d = diameter, r = radius

Volume and Surface Area Formulas: (P = perimeter of base, B = area of base, l = slant height,

h = height)

Shape Lateral Area Surface Area Volume

Rectangular Prism

(Box)

L = Ph (but you must

define the base)

S = 2lw + 2lh + 2wh V = lwh

Prism L = Ph S = L + 2B

S = Ph + 2B

V = Bh

Cylinder L = 2πrh S = L + 2B

S = 2πrh + 2πr2

V = Bh

V = πr2h

Regular Pyramid L =

1

2Pl

S = L + B

S = 1

2Pl + B

V = 1

3Bh

Cone L = πrl S = L + B

S= πrl + πr2

V = 1

3Bh

V = 21

3r h

Sphere NA S = 4πr2

V = 34

3r

sin

cos

tan

oppA

hyp

adjA

hyp

oppA

adj

45°

45° 2a

a

a

30°

60°

a 2a

3a