Analytical Geometry- Common Core Final Exam Preparation

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Name: ___________________________

Geometry Final Exam Review ~ Circles

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

O   x°

2. 12

O

x°

QP

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.

B

O

A

r

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

CK = 14. Find the perimeter of .

L

J

K

O

C

A B

Analytical Geometry- Common Core Final Exam Preparation

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

D

C

BA

P

x°

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

W

Z

X RC

Y

46

95

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

C

A

D

BP

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°.

Analytical Geometry- Common Core Final Exam Preparation

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C

B

A

D )115°

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.)

A

D

C

B

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

A

C

O

B

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

A

C

O

B

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

Y

X

W

Z

26. Name the minor arc and find its measure.

27. Name the major arc and find its measure.

a. m Z

b. m(arc WZ)

c. m W

d. m(arc WX)

Analytical Geometry- Common Core Final Exam Preparation

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28. Find the circumference. Leave your answer in terms of .

18 in.

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 .

8 m

X

Y

P

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.

6 2x

9 x + 6

A

C

B

46º

32º

D 118º

xº

x

A

B

C 120o

190o

Analytical Geometry- Common Core Final Exam Preparation

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36. Find the value of x.

37.

x

10 4

D

E

F

If EF is a tangent line, find x.

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

39. 87. Given: Circle 0 with AE BE

Prove: mAC = mBD

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.

x

A

B

C 115o

200o

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

Analytical Geometry- Common Core Final Exam Preparation

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Geometry Final Exam Review ~ Dilations

In the diagram, the dashed figure is the image of the solid figure.

C

D

F

E

T

S

R

S

R

Q

1. Name the image of E.

2. Name the image of .

1. is a dilation of triangle by a scale factor of ½.

The dilation is centered at the point ( 5, 5). Which statement below is true?

A.

B.

C.

D.

2. is a dilation of triangle by a scale factor of ½.

The dilation is centered at the point (5, 5). What is the ratio of the area of to the area of

A. ½

B. 2

C. ¼

D. 4

Analytical Geometry- Common Core Diagnostic Test -1

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3. Using the study chart above, complete the following:

a. What properties do the dilations have in common with the isometries?

b. Can you make a detailed mind map that compares the different transformations shown

here?

4. In the triangles shown is dilated by a factor of ⅔ to form .

Given that and , what is the ?

A. B. C. D.

5. In is dilated by a factor of ⅔ to form .

Given that and RS = 8 , what is AB ? _________

Line Reflection Translations Rotations Dilations

Isometry Isometry Isometry NOT isometry.

Figures are similar.

Properties preserved: 1. distance

2. angle measure

3. parallelism

4. colinearity

5. midpoint

Properties preserved: 1. distance

2. angle measure

3. parallelism

4. colinearity

5. midpoint

Properties preserved:

1. distance

2. angle measure

3. parallelism

4. colinearity

5. midpoint

Properties preserved:

1. angle measure

2. parallelism

3. colinearity

4. midpoint

Lengths not same.

Reverse Orientation

(letter order changed)

Same Orientation

(letter order the same)

Same Orientation

(letter order the same)

Same Orientation

(letter order the same)

Notation:

Notation:

Notation:

Notation:

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10 yd

3 yd

36 in.

33 in.40 in.

6. If we ,2OD then the correct diagram would be:

Original A) B) C) D)

m

O

m'm

O

m'm

O

m'm

O

m

O

7.

a) This dilation centered at A is a reduction / enlargement b) The ratio of this dilation is ______ : _______ c) Write the dilation using subscripts: __________________

4.5 cm

1.5 cm B'

A B

Geometry Final Exam Review ~ Area

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

1. 2.

3.

9 cm

9 cm 11 cm

8 cm

13 cm

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4.

5.

12.6 in.

29.2 in.

19 in.

14.5 in.

6.

8 in.

7 in.

12 in.

8 in.

Not drawn to scale

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.

1

2

3

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.

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3.6 m

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

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

9

105°

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

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

14. 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?

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

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

17.

a. b. c. d.

perimeter of square is 48 cm

(9,0)

(5,7)

x

y

rectangle

A

45

24 cm 8 cm A

80

A 4 cm

2 cm

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6

8

25

24

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

cube?

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

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

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

22. 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?

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

Geometry Final Exam Review ~ Right Triangles

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

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15

6

Not drawn to scale7 m

8 m

Not drawn to scale

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

3. 4.

.

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.

AB

C

11 ft

Not drawn to scale

8. Find the length of the hypotenuse.

45°

3 2

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

45°

16

Not drawn to scale

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

10.

6 x

60°

12

Not drawn to scale

11.

30°

y

x

17

Not drawn to scale

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

x 34

30°45°

y

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

14. Write the tangent ratios for and .

R Q

P

21

20

29

Not drawn to scale

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Find the value of x to the nearest degree.

15.

11

19

x

Not drawn to scale

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.

Building

100 ft

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.

C B

A

4

3

5

Not drawn to scale

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

19.

x

11

Not drawn to scale

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20.

10

x

Not drawn to scale

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:

23. Which of the following is equal to cos 35

A) sin 35 B) cos 55 C) sin 55 D) cos 145

Geometry Final Exam Review ~ Similarity (Ratio & Proportion)

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

x

8 m

4 m

12 m

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?

4

6

x

30°

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Solve the proportion.

4.

5.

6.

7. . Complete the statements.

D C

E B

A

J

H

G

F

8. Figure . Name a pair of corresponding sides?

10. What is the measure of ?

Q S

R

T V

UU)

)

)) ))63°

47°

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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.

8. 9. 13. 14.

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

You draw the similar triangles and find the other values:

16. List the short-cuts one could use to prove two triangles similar: (3)

17. GIVEN: LN = 4 cm, KL = 5 cm LY = 12 cm, LH = 15 cm

IsKLN HLY ?

12

154

5K

H

L

N

Y

18.

GIVEN: ||TV XP

PROVE:TVY PXYY

T V

X

P

c

a b

n m

h