Geometry Final Exam Review ~ Circles€¦ · Geometry Final Exam Review ~ Congruency 1. Use the figure at the right to complete each of the following statements ... BEC is an isosceles

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Geometry Final Exam Review ~ Congruency

1. Use the figure at the right to complete each of the following statements. ∆𝐴𝐵𝐶 is an isosceles triangle with

BD AC .

a) ADB CDB because they are ________________ angles.

b) BD __________ because of the reflexive property.

c) The triangles are congruent because of _______________ .

d) DBA ______ .

e) CD ____________ because they are corresponding parts of congruent triangles.

f) Point D is the _____________________ of AC .

g) If 42m C , then m A ________.

h) ABD ______________ .

2. If DOG CAT , state whether the following are true or false:

a) O A ________b) DO AT _________ c) OG AT _________ d) G T __________

3. CPCTC represents: _____________ _____________ of ______________ _____________ are

___________.

4. Can the two triangles be proven congruent? If yes, then state the reason, and write the congruency state-

ment.

a) ______, ________ _______________ b) ______, ________ ______________

c) ______, ________ _________________ d) ______, ________ _________________

B

A D C

A

K

C

B

N

M C A

B

A

B

C

P

Q

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5. Given: , .AE DE AEB DEC

Prove: BEC is an isosceles triangle.

6. List 6 pairs of congruent parts for the triangles you proved congruent in #5.

________________________ ________________________ ________________________

________________________ ________________________ ________________________

7. Which of the following can be used to prove triangles congruent? Circle your answers.

SSS SSA SAS AAS ASA AAA HL

Use Scratch Paper

8. Given: Polygon ABCD is a square. Prove .ABC ADC

9. Given: PQR is an equilateral triangle and point S is the midpoint of PR . Prove .PQS RQS

10. Given: ZXW YWX, ZWX YXW

Prove: ZW YX

11. Given: HLS ESL, LHR SER

Prove: SELH

Geometry Final Exam Review ~ Circles

E

A B C D

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Multiple Choice

Identify the choice that best completes the statement or answers the question.

Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x. (Figures are not

drawn to scale.)

____ 1. 111

____ 2. 12

____ 3. is tangent to circle O at B. Find the length of the radius r for AB = 5 and AO = 8.6. Round to the nearest tenth if

necessary. The diagram is not to scale.

____ 5. and are all tangent to O (not drawn to scale). JA = 9, AL = 10, and

CK = 14. Find the perimeter of .

Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.

O   x°

O

x°

QP

B

O

A

r

L

J

K

O

C

A B

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____ 10.

____ 17. and are diameters. Find the measure of arc ZWX. (The figure is not drawn to scale.)

Use the diagram for # 18 - 20. is a diameter, and . The figure is not drawn to scale.

____ 18. Find for = 66.

____ 19. Which statement is NOT true?

a. arc AC arc BD b.

____ 20. Find m(arc BD) for m(arc AC) = 43°.

____ 22. Given that DAB and DCB are right angles and m BDC = 41, what is the measure of arc CAD? (The figure is not

drawn to scale.)

D

C

BA

P

x°

W

Z

X RC

Y

46

95

C

A

D

BP

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____ 23. Find the measure of BAC. (The figure is not drawn to scale.)

____ 24. Find m BAC. (The figure is not drawn to scale.)

25. Given: m X = 150, , m Y = 92. Find each measurement. (The figure is not drawn to scale.)

____ 26. Name the minor arc and find its measure.

____ 27. Name the major arc and find its measure.

Find the circumference. Leave your answer in terms of .

A

D

C

B

A

C

O

B

A

C

O

B

Y

X

W

Z

a. m Z

b. m(arc WZ)

c. m W

d. m(arc WX)

C

B

A

D )115°

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____ 28.

____ 29 The circumference of a circle is 60 cm. Find the diameter, the radius, and the length of an arc of 140°.

____ 30. Find the length of arc XPY. Leave your answer in terms of .

31. The diameter of a wheel on Derrick’s car is 28 inches.

a. How far along the ground does the wheel travel after one complete rotation?

b. If the wheel rolls 140 inches, how many rotations did it complete?

32. Find the value of x. 33. Find the value of x.

34. Find the value of x.

36. Find the value of x.

18 in.

8 m

X

Y

P

6 2x

9 x + 6

A

C

B

46º

32º

D 118º

xº

x

A

B

C 115o

200o

x

A

B

C 120o

190o

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37.

38. Find the value of x in each figure below.

39. 87. Given: Circle 0 with AE BE

Prove: mAC = mBD

x

10 4

D

E

F

If EF is a tangent line, find x.

Statements Reasons

AE BE

Given

AE BE

1.

CEA BED

2.

ACE BDE

3.

AEC BED

4.

AC BD

5.

AC = BD

6.

mAC = mBD

7.

Reason Bank

A. AAS

B. Given

C. CPCTC

D. Inscribed Angles Inter-

cepting Arc Conjecture

E. Definition of Congruent

Arcs

F. Vertical Angle Conjec-

ture

G. Definition of Congruent

H. Reflexive Property

I. Chord Arcs Conjecture

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Geometry Final Exam Review ~ Right Triangles

Short Answer

Find the length of the missing side. Figures are not drawn to scale.

1.

2.

Find the length of the missing side. Leave your answer in simplest radical form.

3.

4.

6

8

25

24

7 m

8 m

Not drawn to scale

15

6

Not drawn to scale

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6. A triangle has sides of lengths 12, 14, and 19. Is it a right triangle? Explain.

7. In triangle ABC, is a right angle and 45. Find BC. Round your answer to the nearest tenth.

8. Find the length of the hypotenuse.

9. Find the length of the leg. If your answer is not an integer, leave it in simplest radical form.

AB

C

11 ft

Not drawn to scale

45°

3 2

45°

16

Not drawn to scale

20 mi

15 mi

Dunlap Butte

Ferris

5. Wayne used the diagram to compute the distance from

Ferris to Dunlap to Butte. How much shorter is the dis-

tance directly from Ferris to Butte than the distance

Wayne found?

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Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.

10.

11.

12. Find the value of x and y, rounded to the nearest tenth.

13. The length of the hypotenuse of a 30°-60°-90° triangle is 4. Find the perimeter.

14. Write the tangent ratios for and .

Find the value of x to the nearest degree.

15.

6 x

60°

12

Not drawn to scale

30°

y

x

17

Not drawn to scale

x 34

30°45°

y

11

19

x

Not drawn to scale

R Q

P

21

20

29

Not drawn to scale

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16. The students in Mr. Collin’s class used a surveyor’s measuring device to find the angle from their location to the top

of a building. They also measured their distance from the bottom of the building. The diagram shows the angle

measure and the distance. To the nearest foot, find the height of the building.

17. A large totem pole in the state of Washington is 100 feet tall. At a particular time of day, the totem pole casts a 249-

foot-long shadow. Find the measure of to the nearest degree.

18. Write the ratios for sin A and cos A.

Find the value of x. Round to the nearest tenth.

19.

Building

100 ft

A249 ft

100 ft

C B

A

4

3

5

Not drawn to scale

x

11

Not drawn to scale

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20.

21. An airlpane pilot sights the top of a control tower at a 22º angle of depression. The airplane is 2000 ft above

the tower. How far is the airplane from the tower?

22. Calculate the value of x:

10

x

Not drawn to scale

4

6

x

30°

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Geometry Final Exam Review ~ Similarity (Ratio & Proportion)

____ 1. The two rectangles are similar. Which is a correct proportion for corresponding sides?

Short Answer

2. A model is made of a car. The car is 9 feet long and the model is 6 inches long. What is the ratio of

the length of the car to the length of the model?

3. The Sears Tower in Chicago is 1450 feet high. A model of the tower is 24 inches tall. What is the

ratio of the height of the model to the height of the actual Sears Tower?

Solve the proportion.

4.

5.

6.

7. . Complete the statements.

8. Figure . Name a pair of corresponding sides?

x

8 m

4 m

12 m

D C

E B

A

J

H

G

F

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10. What is the measure of ?

11. Use the information in the diagram to determine the height of the tree to the nearest foot.

12. Michele wanted to measure the height of her school’s flagpole. She placed a mirror on the ground 48 feet from the

flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her eyes were 5 feet

above the ground and she was 12 feet from the mirror. Using similar triangles, find the height of the flagpole to the

nearest tenth of a foot.

Q S

R

T V

UU)

)

)) ))63°

47°

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15. m = 2, n = 10, b = _____

You draw the similar triangles and find the other values:

8. 9.

13. 14.

c

a b

n m

h

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Geometry Final Exam Review ~ Area

Find the area. The figure is not drawn to scale.

____ 1.

____ 2.

____ 3.

____ 4.

36 in.

33 in.40 in.

10 yd

3 yd

9 cm

9 cm 11 cm

8 cm

13 cm

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____ 5.

____ 6.

____ 7. The area of a parallelogram is 420 cm2 and the height is 35 cm. Find the corresponding base.

___ 8. Given the regular hexagon, find the measure of each numbered angle.

____ 9. Find the area of a regular hexagon with an apothem 16.5 feet long and a side 19 feet long. Round

your answer to the nearest tenth.

Find the area of the circle. Leave your answer in terms of .

____ 27.

12.6 in.

29.2 in.

19 in.

14.5 in.

8 in.

7 in.

12 in.

8 in.

Not drawn to scale

1

2

3

3.6 m

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28. Find the area of the figure to the nearest tenth.

29. Find the area of a sector with a central angle of 180° and a diameter of 5.6 cm. Round to the nearest tenth.

30. Find the area of the shaded region. Leave answers in terms of .

31. A regular polygon has external angles equal to 12. If each edge has a length of 16 inches, what is the length

of the radius?

32. Calculate the area of a regular decagon (10 sides) with edge lengths of 18 cm.

33. Find the area of a regular pentagon that is inscribed in a circle of radius of 10 inches.

34 - Given A. Find the area of the shaded region.

a. b. c. d.

perimeter of square is 48 cm

35 A cube has a volume of 64 cubic meters. Suppose the dimensions are doubled. What is the volume of the new

cube?

36. Find the volume of a cone if its radius is 3 cm and its slant height is 5 cm.

9

105°

(9,0)

(5,7)

x

y

rectangle

A

45

24 cm 8 cm A

80

A 4 cm

2 cm

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37. A cylindrical fish tank is 10 feet in diameter and 6 feet high. How much water can it hold?

38. Find the volume of the sphere if its radius is 3 cm.

39. Plambells makes two different size cans for their chicken noodle soup. Both cans are similar in shape where the

large can is 5 inches tall and the small can is 4 inches tall.

a. If the small can holds 12 ounces of soup, how much will the large can hold?

b. How much more tin is necessary to make the large can compared to the small can?

40. Calculate the ratio of the areas of the two similar figures.