GEOMETRY

SEMESTER 2

REVIEW PACKET

2016

Your Geometry Final Exam will take place on Friday, May 27th, 2016.

Below is the list of review problems that will be due in order to prepare you:

Assignment

# Due Date Homework In-Class

1 Monday, May 23rd #1, 2, 4, 6, 8, 9, 10, 11, 12,

14 #3, 5, 7, 13

2 Tuesday, May 24th #16, 18, 21, 22, 23, 25, 27,

29, 30, 32

#15, 17, 19, 20, 24,

26, 28, 31

3 Wednesday, May 25th #34, 35, 36, 37, 41, 42, 43,

44, 45, 46, 47

#33, 38, 39, 40, 49,

51, 53, 54, 55, 56

4 Thursday, May 26th #48, 50, 52, 57, 58, 59, 60,

61, 62, 63, 64, 70 #65, 66, 67, 68, 69

Your name:___________________________________

Ch 7: Surface Area and Volume

1) A box of tissues measures 5 inches wide, 6 inches high, and 8 inches long.

What is the surface area and volume of the tissue box?

Surface Area = ________________________________

Volume = _____________________________________

2) A cylinder has a height of 6 cm and a base diameter of 10 cm.

a) Find the lateral surface area

b) Find the total surface area

c) Find the volume

3) A pyramid has a square base. Each edge of the base is 4 in, and its slant height is 6 in.

Find its total surface area.

4) Using the following cone, find:

a) its lateral surface area

b) its total surface area

c) its volume

5) This pyramid has a square base with each edge = 12 cm. The height is 8 cm.

Find the total surface area of the pyramid.

6) Pictured at right is a right triangular prism. The height of the prism is 26 cm.

The triangular bases have a base and height of 5 cm and 12 cm. Find the total

surface area of the prism.

7) A cone has a volume of 7,525π m3. If the cone has a height of 25 meters, find the:

a) Lateral surface area

b) Total surface area

8) Find the volume AND total surface area of the figure below.

Ch 8: Circles & Arcs

9) What is the relationship between the measure of a central angle and the measure of its intercepted arc?

10) What is the relationship between the measure of an inscribed angle and the measure of its intercepted arc?

11) What is the relationship between opposite angles in an inscribed quadrilateral? ____________________

12) In Circle Q, 𝑚𝐴𝐵�̂� = 288º and QA = 10.

a. Find the circumference of the circle: _____________

b. Find the area of the circle: ______________

c. Find the length of arc AC: _______________

d. Find the area of the shaded sector AQC: ______________

Round your answer to three decimal places

13) Point C is the center of the circle and AB has a length of 16 cm. Find the area of the shaded region. Round

your answer to three decimal places.

14) Given the regular hexagon below and that 4 cm,PQ find the following:

a. __________m PAQ

b. Apothem = __________________

c. Perimeter = _________________

d. Area = __________________

(round your answer to three decimal places)

15) Find the area of the shaded region. Round your answer to three decimal places:

16) Find the area of sector AB in each problem below. Round your answer to three decimal places:

a. b.

17) If the area of the shaded sector below is 212 ft , find the radius of the following circle. Round your answer

to three decimal places.

18) For Ms. Pinakidis’ birthday, her friends bought her a cookie cake (pictured below) with a diameter of 14 in.

If she cuts the cake into 8 equal pieces and eats 2 pieces to herself, what is the area of the amount of cookie

cake she ate?

19) Given the regular octagon below with a side length of (3 2)x and an apothem of 3, find the value of x if the

area is 221 2.units

20) Solve for x in the circle below.

21) Find the measure and length of each bold arc shown.

a. b.

Arc measure:_________________ Arc measure:_________________

Arc length: __________________ Arc length: __________________

22) Find the value of x: 0(4 36)x

050

(4x+33)o

25o

48o

(2x+13)

23) Find m ABC

a.) b.)

24) In the figure, find the values of x and y. 25)

26) How far is a 12 cm chord from the center of the circle whose radius is 10 cm? Show pictures and justify your

response for full credit.

27) How long is a chord if it is 24 centimeters from the center of a circle whose radius is 26cm? Show pictures

and justify your response for full credit.

28) Two chords are in the same circle with radius 20 cm. One is 16 cm away and one is 10 cm away. Which

chord is longer?

29) a. Find the measure of arc BC

b. Find the length of arc BC

30) a. Find the measure of arc AB.

b. Find the length of 𝐴�̂�.

31) The length of arc AC is 28 cm. Find the measure of the central angle AQC.

Ch 9: Scale Factor and Similarity

32) If the side lengths of two similar polygons have a scale factor of 1

3, what is

a. The ratio of their perimeters?

b. The ratio of their areas?

10 cm 70°

B

A

A

D B

C

7cm

A

D B

C

28cm

7cm

Q

33) Determine if these are scale figures. If so state the scale factor, treating the larger image as the original

figure, and the smaller as the new figure. Fill in all missing angles. If not, change sides to make it a scale

figure, and then state the scale factor.

34) The following are scale figures. State the scale factor, treating the left figure as the original. Then find the

value of x.

35) The two figures below are scale figures. Fill in the missing sides and angles. Round to the nearest

hundredths, if necessary.

12

30

48

24

6

8

5

2 1

4

90 90

90 130

140

8

y

4 x

14

10

36) You scale a polygon by the factor 2

5. You then compare the original polygon to the scaled polygon. Find

the ratio of each pair of measurements.

a. Any two corresponding sides of the polygons _______________________

b. Any two corresponding angles of the polygons ______________________

c. The perimeters of the two polygons _____________

d. The areas of the two polygons _______________

37) Given: ABC DEF

AB = 60 BC = 56 DE = 144 DF = 122.5 mA = 64 mE = 50

a. Find mB: ____________ b. Find mC:______________ c. Find mD:_____________

d. Find mF: ____________ e. Find AC:_______________ f. Find EF:______________

38) Δ𝑄𝑅𝑆 ∼ Δ𝑇𝑈𝑉, QR = 12, RS = 34, UV = 115.6, and TV = 220. Find the perimeter of TUV . Show your

calculations.

39) You are looking up at a statue that is 5 feet away from you. When you look at the top of the statue, you

notice that the top of the statue lines up perfectly with the top of a building. You know the height of the

building is 500 feet and the height of the statue is 10 feet. How far away is the statue from the building?

Hint: Draw a picture.

40) State whether the triangles are similar. Show calculations.

(14, 15)

(14, 11) (8,11) (5, 8)

(5,6) (1, 6)

15

10

5

15 10 5 x-axis

y -axis

C

G

F E

D

B

z

y

x

C

A

B

41)

Ch 10: Trigonometry

42)

43) Express the following in terms of x, y, and z.

a. Side opposite of C:__________

b. Side adjacent to C:__________

c. Hypotenuse:___________

d. sin C:_________ g. sin B:_________

e. cos C:_________ h. cos B:_________

f. tan C:________ i. tan B:___________

44) Which ratio represents tan 𝐴 in ∆ABC? (Circle one)

a. 13

5 b.

13

12 c.

5

12 d.

5

13

45)

46) What is cos 𝑍?

cos 𝑍 = _________________

Reduced fraction ______________

Decimal (to the nearest hundredth) __________________

47) Draw a right triangle that represents the trig ratio 8

tan(71 )x

48) What is cos 72° rounded to 4 decimal places?

__________________________

49) Solve for the measure of angle C if tan C = 1.5497 ______________________

50) 50) Solve for x. Round to 3

decimals

. 51) Solve for z. Round to 3 decimals

52) Solve for y. Round to 3

decimals

53) Solve for c. Round to 3 decimals

54) Solve for the missing angle measures. Round to the nearest degree.

55)

56)

55)

7

53

x

7

34

y

10

z

72

_

_ _ _

41

19

c

10

7

y

56) Andrew is standing at point B, looking up at an airplane in the sky. The angle of elevation (from B

to A) is 55 . What is the direct distance from Andrew to the airplane?

Ch 11: Transformations and Coordinate Geometry

57)

58) List two transformations that preserve congruency:

59) Which transformation creates an image that is similar to the pre-image?

60) What is the relationship between slopes of parallel lines?

61) What is the relationship between slopes of perpendicular lines?

55

62) Describe the transformation, then write a rule to represent the transformation

63) Describe the transformation, then write a rule to represent the transformation

64) Using the graph below, what is the rule for a translation from point A to point D?

(a) 1,4, yxyx (c) 1,4, yxyx

(b) 4,1, yxyx (d) 4,1, yxyx

65) Graph the quadrilateral ABCD with 2,2A

, 5,1B

, 6,4C

, and 3,7D

.

a. ABCD is translated to produce A B C D . The translation is defined by the following rule:

, 7, 2x y x y . Graph A B C D and list

the coordinates below:

A’ = ___________

B’ = ___________

C’ = ___________

D’ = ___________

b. Describe the translation in words:

66)

67) For the points A(-5,6) and B(15,-54)

a. Find the distance between A and B

b. Find the midpoint of AB

c. Write the equation of a line that passes through A and B

d. Write an equation of a line that is parallel to AB

e. Write an equation of a line that is perpendicular to AB

68) Rewrite each equation in slope intercept form, then graph.

a.) 10 15 30x y b.) 9 12 36x y

69)

70)