**THERE ARE 10 PROBLEMS IN THIS REVIEW PACKET THAT ARE

IDENTICAL TO 10 OF THE PROBLEMS ON THE FINAL EXAM!!!**

Your exam is on Chapters 7 – 12. Don’t forget to study Surface Area & Volume (it is not in this

packet, but will be covered on the exam!)

NOTE: For additional preparation go to classzone.com or your textbook pp.815-826. Answers to odd

problems are in the back of the book.

Note: figures may not

be drawn to scale

NAME:____________________________________ TEACHER:_________________________________ PERIOD:__________________________________ My EXAM DATE:____________________________ My EXAM TIME:____________________________

REMINDER: please bring your textbook to the Exam

2

Chapter 7 1. Match the transformation with the picture that maps figure I onto figure II. ROTATION a) TRANSLATION b) REFLECTION c) GLIDE REFLECTION d) The above transformations are all isometries because, in each, the preimage and image are

. 2. Complete the statements below regarding the transformation shown.

a. ∆ABC →∆______

b. ∆______ →∆EDF c. ∠ A → ∠ ______

d. BC = ______

e. m∠ D = _______o

3. Use the graph of the isometry below. ABCD is the preimage.

a. Figure ABCD → Figure______ b. Identify the isometry shown ________ c. Name the image of CD ______

d. Identify the center of this rotation ________

I

I

I

I

II

II

II

II

3

4. Find the value of each variable below.

5. Give the coordinates of the image of (3, 2) when reflected in:

a. The x axis ____________

b. The y axis ____________

c. The line x = –1 __________ d. The line y = 4__________

4

6. At right ∆ABC is mapped onto ∆A”B”C” by a rotation.

a. Determine how many degrees and direction of the rotation. b. Identify the center of rotation.

A

B

C

A’

B’ C’

A”

B”

C”

142o

O

5

7. In the diagram below there is a distance of 4 cm between lines l and m. ∆ABC was

reflected in line l, and ∆A’B’C’ is reflected in line m.

a. Identify the transformation that maps �ABC→�A′′B′′C′′. __________________ b. What is the distance between points A and A′′. ___________________

c. What other segments are congruent to AB. _____________________

d. What line is the perpendicular bisector of CC′. ___________________

8. Using vector 6,3 translate ∆XYZ below.

9. Write the vector from # 8 in coordinate notation. _________________________

m l

A”

C” C’ C B” B’ B

A’ A

6

10. Glide Reflections are composites of two transformations, ____________________ and _______________________.

11. Choose the transformation below that depicts a Glide Reflection. a. b. c.

12. Choose the notation below that describes the translation.

a. (x, y) → (x – 3, y + 4)

b. (x, y) → (x – 3, y - 4)

c. (x, y) → (x – 4, y + 3)

d. (x, y) → (x – 4, y - 3)

e. (x, y) → (x + 4, y + 3)

13. Use the figure below to determine which segment represents a 90o counter-clockwise

rotation of FE about P.

7

Chapter 8

1. Solve the proportions.

a) y = 4 b) 7 = 4 9 6 3n + 5 n

2. The ratio of the two side lengths of the triangle is given. Solve for the variable.

a) AB:BC is 2: 5 b) MN:MO is 3:4 3. The lengths of the sides of a triangle are in the extended ratio of 2:3:5. If the perimeter

is 70 inches, find the lengths of each side.

Equation: ______________________ Sides: ________ , ________, ________

A

B C 20

x O

N

M

9

x

8

4. Find the geometric mean of the two numbers.

5 and 20 4 and 9 5. Given: ∆ABC ~ ∆DEC, and BE = 6, EC = 8, DC = 10 and AB = 12.25

Find the lengths of DE and AD

a. Find DE DE= _______ b. Find AD AD= _______

6. In the diagram below, parallelograms RSTU � LMNO.

a) Find the ratio of sides of RSTU to LMNO. b) Find the ratio of sides of LMNO to RSTU.

c) Find LM

d) Find m∠O

e) Find the ratio of the perimeter of parallelogram RSTU to the perimeter of parallelogram LMNO.

R

U

S

T

12

9

L

O

M

N 72°

3

A

B

E

C D

6

8

10

12.25

9

7. Use the pairs of triangles below. a) Decided if the triangles below are similar. b) If yes, state the postulate or theorem and use proportions if necessary. c) If the triangles are similar write a similarity statement.

8. Determine whether the given information implies BC // DE. Explain your answer. (Figure not drawn to scale) 9. Last December, the exchange-rate for Canadian dollars to American dollars was

$1.47 Canadian to $1.00 American. If you paid $55.00 Canadian dollars for a sweatshirt, what did the shirt cost you in American dollars?

10. A 5 x 7 inch photo is being enlarged by a scale factor of 117

. What are the dimensions

of the enlarged photo? Round your answers to the nearest tenth.

_______ in. by _______ in.

A

D E

6 4

B C

6 9

10

11. Use your knowledge of similar triangles and proportionality theorems to find the values of the variables below.

a) Given: ∆ABC � ∆DEC find the value of x and y.

b) Given: WX bisects ∠ X find the value of a.

c) Find the value of a in the figure below.

11

12. The larger triangle is an enlargement of the smaller triangle. What is the scale factor? Solve for x and y.

13. Use the given scale factors to find the coordinates of the vertices of the image of the

∆ XYZ.

k = 2 X ( ___, ___)

Y ( ___, ___)

Z ( ___, ___)

X’ ( ___, ___)

Y’ ( ___, ___)

Is this an enlargement Z’ ( ___, ___) or a reduction? (Circle one.)

k = ½

X ( ___, ___)

Y ( ___, ___)

Z ( ___, ___)

X’ ( ___, ___)

Y’ ( ___, ___)

Is this an enlargement Z’ ( ___, ___) or a reduction? (Circle one.)

12

Chapter 9

1. Find the unknown side length of the right triangles below using the Pythagorean

theorem. Then find the perimeter of each triangle x = _______ x = _______ perimeter = _______ perimeter = _______ 2. Which can be the lengths of the sides of a right triangle? _____

a) 8, 31, 32 b) 16, 20, 36

c) 1, 2, 5 d) 3 , 4 , 5

3. Which of the above could not make ANY type of triangle (acute, obtuse, or right)? 4. You are setting up your volleyball net. The top of the pole of the net is 7 feet high. A

stake is put in the ground 3 feet from the base of the pole. You need to determine how much rope is needed to connect the pole with the stake. What is the distance from the top of the pole to the stake in the ground? (Give your answer to the nearest tenth.)

Equation: _____________________

Answer: ________________

6

8

x

13

x

5

Make sure you are in degree mode.

13

5. Use special right triangles to find the value of each variable. Write answers in simplest radical form.

a) b) c)

6. Find the length of w, x, y and z . Give exact answers (keeping any radicals).

w = ________

x = ________ y = ________ z = ________

7. Use a calculator to approximate the given value to 4 decimal places.

a) tan 420 b) cos 650 c) tan 140 d) sin 830

45°

60°

30°

x

y

z 50

w

10

x

y

14

For 8 through 11 write the trig equation (proportion), and find x to the nearest tenth. 8. Trig equation ________________ x = _____________ 9. Trig equation ________________ x = _____________ 10. Trig equation ________________ x = _____________ 11. Trig equation ________________ x = _____________

x

20

x 20

x

20

x

75

400

400

350

20

750

x

15

12. Use the right triangle find the length of x. Express each trig function as a ratio in simplest form.

a) x = _________ b) sin C = _________ c) cos C = _________ d) tan A = _________ 13. The wire support for a telephone poll is 60 feet long. If the angle of elevation of the

wire is 25 degrees, how tall is the telephone poll? (Hint: draw a triangle diagram) Show trig equation used and solution. Express your answer to the nearest tenth.

Trig Equation: _________________

Answer: ________________ 14. Write a trig equation to find the measure of angle A in the triangles below. Round

decimals to the nearest tenth. a) b) c) Trig Equation: ___________ Trig Equation: ___________ Trig Equation: ___________

Answer: _________ Answer: _________ Answer: _________

A

8 12

A

8

11 A

7

23

A

B C

x

24

26

16

Chapter 10 1. Match the term with the best notation that describes it.

_____Center �BDE

_____Chord CE _____Diameter C

_____Radius BD

_____Point of Tangency ∠DBE

_____Secant BE

_____Central angle BD����

_____Inscribed angle �ABE

_____Major arc ∠BCA

_____Semicircle �AE _____ Minor arc E

2. Is AB tangent to circle C ? Explain your answer. 3. AB and AD are tangent to circle C. Find the value of x.

4. MQ and NR are diameters. Find and measures below.

m �MQN = ______

m �NQ = ______

m �NQR = ______

m ∠MOR = ______

***Circles are not drawn to scale.***

17

5. Find the indicated measure for circle P.

a. DC = ______

b. �mDC = ______

6. Find the measure of �MN .

a. b. c.

7. Find the measure of the indicated arc or angle.

�mPQ = ______

m ∠QNP = ______

m ∠QNO = ______ 8. Find the value of x and y.

600

18

9. Find the measure of ∠1 in each figure below. 10. Solve for x in the figures below. Show your equation and calculations.

1800

x

380

1150

1050

x

104

x

1

260o

1

128o 1

33o 131o

1040

19

11. Using the circle equations, give the center and radius of the circle.

a. x2 + y2 = 9 center = ( , ) ; radius =_________ b. ( x - 2 )2 + ( y - 4 )2 = 16 center = ( , ) ; radius =_________ c. ( x + 4 )2 + ( y - 2 )2 = 25 center = ( , ) ; radius =_________

12. Write the standard equation of a circle with the given center and radius.

a. center = ( 0 , 4 ) ; radius = 4 equation ___________________________ b. center = ( -1 , 2 ) ; radius = 12 equation ___________________________ c. center = ( -3 , -5 ) ; radius = 5 equation ___________________________

13. Write the standard equation of the circle with the center ( - 4, 2 ) and point (-7, 6 ) on the circle.

14. Is the point (0, –1) on the circle with equation ( x + 4 )2 + ( y – 2 )2 = 25?

20

Chapter 11 1. Find the sum of the measures of the interior angles of a regular hexagon. 2. Use the polygons below to find the value of x.

3. Identify the regular polygon that has a measure of 108 for each of its interior angles.

a. Pentagon b. Octagon c. Decagon d. Hexagon 4. Find the sum of the measures of the exterior angles of the following regular polygons.

a. Hexagon b. 20-gon 5. Find the area of the equilateral triangle below.

5ft.

5ft.

5ft.

21

6. Find the area of the regular pentagon below. a. Find the length of the side of the pentagon (nearest hundredth) s = ________ b. Find the area of the pentagon (nearest hundredth) A = ________ 7. Given a regular octagon with apothem of 6 cm a. Find the measure of a central angle of the octagon ________ b. Find the length of the side of the octagon (nearest hundredth) s = ________ c. Find the perimeter of the octagon (nearest hundredth) P = ________ d. Find the area of the octagon (nearest hundredth) A = ________

4in 36

o

22

8. A heptagon has one side length of 15 inches. Another similar heptagon has a corresponding side length of 12 inches. Find the ratios of their perimeters of of the smaller to the larger heptagon. a. 16: 25 b. 4:5 c. 15:12 d. 25:16 e. 5:4 9. The two boxes shown are similar. a. Find the ratio of their heights, small to large. _____ : _____ b. Find the ratio of the area of their tops (shaded), small to large. _____ : _____ 10. The two triangles below are similar. The height of the larger triangle is five times

longer than the smaller triangle. Given the area of the smaller triangle is 9 cm2 find the area of the larger triangle.

a. 18 cm2 b. 45 cm2 c. 225 cm2 d. 200 cm2

4

5 5 12

15 15

3

15

23

11. Find the circumference of the circle.

12. Find the radius of the circle whose circumference equals 26π.

13. Find the length of �AB in the circle below. 14. Find the circumference of the circle below.

6

120 6

A

B

A

B

600

15

24

15. Find the area of the circle below. Leave your answer in terms of π . 16. Find the area of the shaded region of the circle below.

17. A square with area 36 inches2 is circumscribed about a circle.

a. Find the circumference of the circle. Leave your answer in terms of ππππ.

b. Find the area of shaded region. Express your answer to the nearest tenth.

18. Find the probability that a point chosen at random in parallelogram ABCD lies in the shaded region.

8cm.