Mastering the EOI, Geometry, SE - Glencoe

Includes:

• Student Recording Sheet for Mastery• Diagnostic Test• Practice by Objective• Practice Test

Diagnose • Prescribe • Practice for the End of Instruction

Geometry

the EOI

OKcover_GEO_SE_894014.indd 1 7/3/09 1:35:21 PM

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior permission of the publisher.

Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240-4027

ISBN: 978-0-07-894014-9MHID: 0-07-894014-1 Mastering the EOI, Geometry

Printed in the United States of America.

1 2 3 4 5 6 7 8 9 10 009 18 17 16 15 14 13 12 11 10

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Contents

Diagnostic Test—Student Recording Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Diagnostic Test—Student Answer Document . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Diagnostic Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Practice by Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Practice Test—Student Answer Document . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

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Mastering the EOI, Geometry iii

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Color in the bubble for each question that you answered correctly on the Diagnostic Test. For each question you did not answer correctly, your teacher may ask you to do the exercises on the practice page(s) listed from this workbook.

Question Objective Assessed Practice Page

1 G.2.6.b 25

2 G.2.5.b 23

3 G.1.2 12

4 G.3.2 27

5 G.5.1 34

6 G.2.6.a 24

7 G.4.2.b 32

8 G.2.3.c 18

9 G.2.2.b 14

10 G.2.4.a 20

11 G.4.1.b 30

12 G.2.4.b 21

13 G.2.3.a 16

14 G.3.3 28

15 G.2.3.b 17

16 G.2.2.a 13

17 G.5.2.a 35

Question Objective Assessed Practice Page

18 G.1.1 11

19 G.3.1 26

20 G.5.2.b 36

21 G.2.2.c 15

22 G.4.2.a 31

23 G.2.5.a 22

24 G.4.3 33

25 G.2.3.d 19

26 G.4.1.a 29

27 G.2.6.b 25

28 G.3.2 27

29 G.2.3.c 18

30 G.4.1.b 30

31 G.2.6.a 24

32 G.5.1 34

33 G.2.2.c 15

34 G.2.3.d 19

Diagnostic TestStudent Recording Sheet

How many did you answer correctly? __________________

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Mastering the EOI, Geometry v



Record your answers by coloring in the appropriate bubble for the best answer to each question.

1 A B C D

2 F G H J

3 A B C D

4 F G H J

5 A B C D

6 F G H J

7 A B C D

8 F G H J

9 A B C D

10 F G H J

11 A B C D

12 F G H J

13 A B C D

14 F G H J

15 A B C D

16 F G H J

17 A B C D

18 F G H J

19 A B C D

20 F G H J

21 A B C D

22 F G H J

23 A B C D

24 F G H J

25 A B C D

26 F G H J

27 A B C D

28 F G H J

29 A B C D

30 F G H J

31 A B C D

32 F G H J

33 A B C D

34 F G H J

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Diagnostic TestStudent Answer Document

Mastering the EOI, Geometry 1

01_OK_EOI_SAD_894014.indd 1 6/3/09 12:31:26 PM

7/3/09 1:44:00 PM002_OK_EOI_SAD_8.indd2

3 Oklahoma has the longest education commitment of any state in the nation. If a person in Oklahoma is from age 5 to 18, then they are required to attend school.

Which of the following is the contrapositive of the above statement?

A If a person in Oklahoma is required to attend school, then they must be from age 5 to 18.

B If a person in Oklahoma is not required to attend school, then they are not from age 5 to 18.

C If a person in Oklahoma is not from age 5 to 18, then they are not required to attend school.

D A person in Oklahoma will attend school if and only if they are from age 5 to 18.

G.1.2

4

G.3.2

In radical form, what is the perimeter of this rectangle?

F 9 + 9 √ � 3 G 18 + 18 √ � 3 H 36

√ � 2

J 36 √ � 3

18

30°

18

30°

1

G.2.6.b

Chords −−

KL and −−−

MN intersect at point O in the interior of a circle. If KO = 9, LO = 4, and MO = 3, then what is the value of NO?

· = ·AE · EC = BE · ED

A 6.8 C 10B 8 D 12

2 Triangles XYZ and MNP are congruent.

What is the perimeter of �XYZ?

F 19 mm H 42 mmG 23 mm J 52 mm

8 mm

19 mm

15 mm

8 mm

19 mm

15 mm

G.2.5.b

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Diagnostic Test

03_10_OK_DT_894014.indd 3 6/16/09 10:33:15 AM

8

G.2.3.c

ABCD is a rectangle and AC = 3x + 1.

What is the value of x?

F 4

G 4 2 _ 3

H 5 1 _ 3

J 13

5

12

5

12

9

G.2.2.b

Line t intersects lines a and b.

(3x)°

(2x)°

a

b

t

What value of x will guarantee that a || b?

A 0B 18 C 36D 90

7 Mr. Siefke’s class has built two congruent square-based pyramids. The area of the base of the first pyramid is 400 square inches. The height of the second pyramid is 30 inches. What is the volume of the first pyramid?

A 4,000 cu in.B 6,000 cu in.C 12,000 cu in.D 1,600,000 cu in.

G.4.2.b

5

G.5.1

Line r passes through points (2, -1) and (-4, 0). Line s is perpendicular to line r. What is the slope of line s?

A -6 C 1 _ 6

B - 1 _ 6 D 6

6 Triangle FGH is inscribed in the circle with center A, m � FH = 156°, and m � GH = 116°.

What is m∠FHG?

F 88°G 64°H 44°J 32°

G.2.6.a

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4 Mastering the EOI, Geometry

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Diagnostic Test (continued)

03_10_OK_DT_894014.indd 4 6/17/09 12:52:27 PM

13

G.2.3.a

Which type of polygon is represented by the star in the Great Seal of the State of Oklahoma?

A decagonB dodecagonC pentagonD hexagon

12

G.2.4.b

Ken has a fence around his triangular garden as shown.

If he makes a scale drawing of his garden and the longest side has a length of 4 inches, what is the length of the shortest side on the drawing?

F 1.75 in. H 3 in.G 2 in. J 3.42 in.

20.5 ft 10.5 ft

24 ft

20.5 ft 10.5 ft

24 ft

11

G.4.1.b

How many square inches of leather are needed to cover a basketball that is 10 inches in diameter?

A 80π sq in.B 100π sq in.C 400π sq in.D 1,600π sq in.

SA = 4π r 2 SA = 4π r 2

10 In the triangles, ∠B � ∠E.

Which of the following is sufficient to prove that the triangles are similar?

F ∠A � ∠C

G AB _ DE

= AC _ DF

H ∠A � ∠E

J AB _ BC

= DE _ EF

G.2.4.a

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16

G.2.2.a

In the figure below, line m is parallel to line n.

40°

130°

m

n

What is the measure of ∠ACB?

F 10°G 50°H 90°J 130°

15

G.2.3.b

In triangle XYZ, ∠Z is a right angle and m∠Y = 37°. Which of the following is the measure of ∠X?

A 43°B 53°C 96°D 143°

17

G.5.2.a

y

x

Which name best describes quadrilateral WXYZ?

A parallelogramB rectangleC squareD rhombus

14 The figure below shows a 10-foot ladder leaning against a wall. The ladder makes a 62° angle with the ground.

To the nearest tenth of an inch, how high does the ladder reach?

cos 62° = 0.47

sin 62° = 0.88

tan 62° = 1.88

F 4.7 ftG 5.3 ftH 8.8 ftJ 18.8 ft

? 10 ft

62°

? 10 ft

62°

G.3.3

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03_10_OK_DT_894014.indd 6 6/16/09 10:33:23 AM

20

G.5.2.b

y

x

If trapezoid LMNP is reflected across the y-axis, what will be the coordinates of L’?

F (-5, -1) G (5, 1) H (1, 5) J (-1, 5)

21

G.2.2.c

Lines m and n intersect at point T, m∠1 = x - 2, and m∠2 = 2x + 5.

21 3

What is the measure of ∠1?

A 57°B 59°C 123°D 180°

18 The Venn diagram shows the results of Martha’s poll of local pet owners.

DogOwners

CatOwners

Which statement is not justified by the diagram?

F 25 people were surveyed.G 14 people have only dogs.H 4 people have no cats or dogs.J 2 people have both cats and dogs.

G.1.1

19

10

5

What is the measure of −−

XZ to the nearest tenth?

A 5.0B 8.7C 11.2D 15.0

G.3.1

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03_10_OK_DT_894014.indd 703_10_OK_DT_894014.indd 7 6/18/10 1:12:41 AM6/18/10 1:12:41 AM

24

G.4.3

Top

Side Front

Which of the following is the side view of the solid above?

F H

G J

23

G.2.5.a

In quadrilateral ABCD, −−

AB � −−

CD and

−− AC �

−− BD .

Which postulate can be used to prove �ABD � �DCA?

A SASB ASAC SSSD AAS

22

G.6.4.a

The two cylinders are similar.

6 cm h

If the volume of cylinder A is 270 cubic centimeters and the volume of cylinder B is 1250 cubic centimeters, what is the height, h, of cylinder B?

F 3 cmG 5 cmH 6 cmJ 10 cm

25 The dome atop the Oklahoma State Capital was completed in 2002. At its base it is 80 feet in diameter. To the nearest foot, what is the circumference of the base of the dome?

(Use π = 3.14.)

A 20,096 ftB 5,024 ftC 251 ftD 126 ft

G.2.3.d

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03_10_OK_DT_894014.indd 8 6/16/09 10:33:32 AM

27 In the circle, m � BD = 64°, m � BC = 96°, secant � � BC and tangent � � AD intersect at point A.

What is m∠DAB?

m∠QPS = 1 _ 2 (m � RT - m � QS )

A 68°B 100°C 136°D 200°

G.2.6.b

29

G.2.3.c

5x � 3

2x + 12

If MNPR is a rhombus, what is the measure of

−− RP ?

A 5B 18C 22D 88

28

G.3.2

In right triangle FGH, ∠F � ∠G and FG = 20.

What is the value of FH?

F 10G 10 √ � 2 H 20 √ � 3 J 40

26 What is the total number of faces and edges for a triangular pyramid?

F 4G 9H 10J 14

G.4.1.a

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03_10_OK_DT_894014.indd 9 6/16/09 10:33:37 AM

30

G.4.1.b

12 in.

3 in.8 in.

When filled to the top, how many cubic inches of Morning Crunch cereal will this box hold?

V = �wh

F 312 in 3 G 288 in 3 H 156 in 3 J 96 in 3

31

G.2.6.a

The center of this circle is P, m∠APB = 35°, and m � CD = 50°.

What is m∠CPB?

A 35°B 50°C 85°D 95°

32

G.5.1

The center of this circle is P.

When placed on a coordinate plane, point P has coordinates (-2, 1) and point R has coordinates (-5, 5). What is the radius of circle P?

F 3 H 10G 5 J 25

33

G.2.2.c

Line t is perpendicular to line �.

t20°65°

�

What is m∠DGB?

A 25° C 135°B 70° D 160°

34

G.2.3.d

A square has an area of 49 square meters. What is the perimeter of the square?

F 14 m H 49 mG 28 m J 98 m

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3 The table shows the maximum number of intersections possible with 2, 3, 4, 5, and 6 segments. How many intersections do you think would be possible with 8 segments?

A 21 C 30B 28 D 32

Number of segments

2 3 4 5 6

Number of intersections

1 3 6 10 15

Number of segments

2 3 4 5 6

Number of intersections

1 3 6 10 15

2 A famous and useful sequence in mathematics is the pattern of numbers shown. What is the tenth number in the pattern?

1, 1, 2, 3, 5, 8, 13, …

F 21 H 55G 34 J 89

1 If one pair of opposite sides of a quadrilateral is parallel, and the other pair is congruent, then the quadrilateral is a parallelogram.

Which figure can be a counterexample to the conjecture above?

A rectangleB rhombusC regular pentagonD isosceles trapezoid

4 The Venn diagram below shows the relationship among quadrilaterals. Which statement is not correct?

F All rectangles are parallelograms.G Some rhombi are squares.H Some trapezoids are

parallelograms.J No rectangles are trapezoids.

5 If you live in Cimarron county, then you are bordered by five states. Ian lives in a county bordered by three states. Which is a correct conclusion ?

A Ian does not live in Cimarron county.

B Ian lives in New York.C Ian lives in Cimarron county.D Ian does not live in Oklahoma.

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Practice by ObjectiveG.1.1

11_36_OK_EOI_PbyO_894014.indd 11 6/23/09 2:25:06 PM

1 If x = 12, then 5x = 60.

Which of the following is the contrapositive of this statement?

A If x ≠ 12, then 5x ≠ 60.B If x = 12, then 5x ≠ 60.C If x ≠ 12, then 5x = 60.D If 5x ≠ 60, then x ≠ 12.

5 Using the Commutative Property of Addition where a, b, and c are real numbers, the statement below is true.

If a + b = c, then b + a = c.

Which of the following is correct?

A The converse of the given statement is never true.

B The contrapositive of the given statement is never true.

C The inverse of the given statement is never true.

D The inverse of the given statement is always true.

3 If the sum of the measures of 2 interior angles of a triangle is less than 90°, the triangle is obtuse. In �ABC, m∠B = 47° and m∠C = 42°.

Which of the following is a valid conclusion from these two statements?

A ∠B � ∠AB ∠A is a right angle.C AC > BCD �ABC is an obtuse triangle.

2 If M is the midpoint of −−XY , then

XM = MY.

Which of the following is the converse of this statement?

F If XM = MY, then M is the midpoint of

−−XY.

G If M is not the midpoint of −−XY ,

then XM ≠ MY.H M is the midpoint of

−−XY if and

only if XM = MY.J If XM ≠ MY, then M is not the

midpoint of −−XY.

4 If points A, B, and C are collinear, then A, B, C are coplanar.

Which of the following statements is logically equivalent to the conditional statement above?

F If points A, B, and C are not collinear, then A, B, C are not coplanar.

G If points A, B, and C are not coplanar, then A, B, C are not collinear.

H If points A, B, and C are not coplanar, then A, B, C are collinear.

J If points A, B, and C are coplanar, then A, B, C are collinear.

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2 East of Oklahoma City, route 66 cuts across routes 177 and 377 approximately as shown below.

(x + 89)°

(5x � 3)°

US 377US 177

US 66

If routes 177 and 377 are parallel to each other, what is the value of x?

F 15 2 _ 3

G 23H 112J 180

3 Parallel lines a and b are cut by transversal t .

t

a

b

Which pair of angles must have the same measure?

A ∠MHY and ∠MJDB ∠MHY and ∠MHXC ∠YHN and ∠HJDD ∠XHJ and ∠XHM

4 Lines � and m are parallel.

�

m

1 2

43

5 6

87

Which pair of angles is supplementary?

F ∠1 and ∠6G ∠2 and ∠3H ∠3 and ∠7J ∠4 and ∠5

1 In the diagram, m ‖ n and p ⊥ n .

p q

m

n5 13

Which of the following must be a true statement?

A p ‖ qB m∠5 = m∠13C q ⊥ nD p ⊥ m

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Practice by ObjectiveG.2.2.a


1 Transversal t cuts lines m and n.

t

m

n7

658

4 321

Which of the following verifies that m and n are parallel?

A m∠4 + m∠6 = 180°B m∠2 + m∠8 = 90°C m∠3 + m∠6 = 180°D m∠2 + m∠6 = 180°

2 Transversal t cuts lines m and n.

t

m

n(x + 25)°

(3x � 17)°

For what value of x will lines m and n be parallel?

F 4G 21H 43J 46

3 Which of the following guarantees that a pair of lines in the plane cut by a transversal are parallel?

A A pair of alternate interior angles are supplementary.

B A pair of alternate exterior angles are complementary.

C A pair of consecutive interior angles are supplementary.

D A pair of corresponding angles are supplementary.

4 Line t intersects lines m, n, �, and p.

m

t

n � p

110°

110° 90° 70°

Which of the following is a true statement?

F m ‖ nG p ⊥ tH m ‖ pJ n ‖ p

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Practice by ObjectiveG.2.2.b


1 Lines m and n intersect and form the indicated angles.

m

n

(2x + 21)°

(4x � 3)°


A 9B 12C 27D 33

2 In the diagram below, m∠ACT = 130°, m∠GCT = 62°, and ∠BCT is a right angle.

Which of the following is the measure of ∠ACG?

F 68°G 74°H 102°J 158°

3 The measures of two supplementary angles are given by (3x + 7)° and (2x + 3)°. What is the measure of the smaller angle?

A 16°B 35°C 71°D 109°

4 In the diagram below, −−

AD ⊥ −−

CF , −−

GH bisects ∠FGE, and m∠BGC = 38°.

What is the measure of ∠BGE?

F 104°G 142°H 166°J 180°

5 The measure of the larger of two adjacent angles is 12 degrees more than three times the measure of the smaller angle. If the two angles are also supplementary, what is the measure of the smaller angle?

A 42°B 56°C 64°D 138°

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Practice by ObjectiveG.2.2.c

11_36_OK_EOI_PbyO_894014.indd 15 6/24/09 10:18:11 AM

1 Which of the following polygons has exactly 8 sides?

A a decagonB an octagonC a heptagonD a dodecagon

2

11

8

Which term best describes the polygon shown above?

F concaveG regularH pentagonalJ convex

4 The map of Oklahoma most closely resembles a hexagon.

Oklahoma

Which two words best describe this shape?

F regular and convexG regular and concaveH irregular and convexJ irregular and concave

3 Which of the following is not a true statement for a regular convex hexagon?

A It has 6 sides.B All the interior angles have equal

measure.C The perimeter is 6 times the

length of any side.D At least one diagonal is outside

the hexagon.

5 Which of the following figures is an example of a concave polygon?

A

B

C

D

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1

31°

88°

x°


A 61B 92C 119D 149

3(x + 22)°

138°

x°

What is the measure of ∠KLM in the diagram above?

A 22°B 68°C 100°D 122°

2 What is the measure of each exterior angle of a regular decagon?

F 18°G 36°H 90°J 144°

5 Quadrilateral PQRS has interior angle measures as shown.

(x � 15)°

27°93° (2x)°


A -15B 65C 70D 85

4 A regular pentagon is shown below.

(x � 31)°


F 41G 72H 77J 103

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2 Quadrilateral RTSQ is a rhombus.

52°

What is the measure of ∠ATS?

F 38°G 48°H 52°J 90°

3 In trapezoid AURQ, −−

AU ‖ −−

QR and X and Y are the midpoints of

−− AQ

and −−

RU .

10

7

Which is the length of −−

QR ?

A 4B 7C 8D 8.5

4 Quadrilateral ABCD is a rectangle with AC = 26 and AD = 10.

Which is the length of −−

BE ?

F 5G 13H 24J 26

1 Quadrilateral PQRS is a parallelogram with PT = 3x + 5 and RT = 7x - 11.

Which of the following equals PR?

A 4B 17C 34D 42

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Practice by ObjectiveG.2.3.c

11_36_OK_EOI_PbyO_894014.indd 1811_36_OK_EOI_PbyO_894014.indd 18 6/17/10 4:08:55 PM6/17/10 4:08:55 PM

1 The Oklahoma state highway markers can be approximated by a square. Suppose the highway department needs to replace markers along route 99. The markers are 3 feet by 3 feet and are to be painted white before being detailed with black paint.

If a gallon of paint covers 300 square feet, how many gallons of white paint are needed to paint 100 markers?

A 1B 2C 3D 9

2 A charcoal grill has a circular grill top that is 22 inches in diameter. What is the cooking area of the grill top?

F 22π square inchesG 121π square inchesH 380π square inchesJ 484π square inches

4 Rectangle ABCD has a length of 24 units and a width of 16 units.

What is the area of the inscribed rhombus MNOP?

F 48 square unitsG 96 square unitsH 192 square unitsJ 384 square units

3 In the trapezoid below, −−

AB ‖ −−

CD .

4.5 in

4 in.

6 in.5 in.

9 in.

What is the area of trapezoid ABCD?

A 20.25 square inchesB 22.5 square inchesC 29.25 square inchesD 40.5 square inches

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Practice by ObjectiveG.2.3.d


2 Triangles ABC and JKL are similar.

995 48°

48°

What is the m∠B?

F 5°G 48°H 66°J 132°

3

Which of the following is not enough to prove that �KLM is similar to �PQR ?

A PQ _ KL

= QR _ LM

= PR _ KM

B PQ _ KL

= QR _ LM

and ∠Q � ∠L

C ∠Q � ∠L and ∠P � ∠K

D PQ _ KL

= QR _ LM

1

Which of the following would be enough to prove that triangles CDT and RST are similar?

A ∠SRT � ∠STRB ∠SRT � ∠DCTC

−− RC �

−− CT

D −−

SD � −−

DT

4 The triangles below are similar.

7.54.5

53

Which statement is true?

F −−

GR � −−

NV

G NV _ GR

= 1.5

H ∠G � ∠V

J NV _ GR

= 2 _ 3

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1 In the diagram below, triangles CFH and CRS are similar.

10

3114°

4

58

14

Which of the following is the length of

−− RS ?

A 6 1 _ 2 C 7 3 _

4

B 7 1 _ 2 D 13 1 _

4

2 The triangles below are similar.

8

45


F 9G 10H 16J 25

3 The perimeters of two similar rectangles are in a ratio of 16 to 9. What is the ratio of the area of the larger rectangle to the area of the smaller rectangle?

A 4 to 3B 16 to 9C 32 to 18D 256 to 81

4 A company makes a car flag that is similar in shape to the most popular size Oklahoma state flag shown below.

5 ft

3 ft

If the car flag has a length of 12 inches, what is its width?

F 7.2 in.G 10 in.H 14 in.J 20 in.

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1

Which of the following data sets can be used to prove that �DEF and �RPK are congruent?

A −−

EF � −−

PK , ∠E � ∠P, ∠F � ∠KB

−− EF �

−− PK , ∠D � ∠R

C −−

EF � −−

PK , −−

DE � −−

RP , ∠F � ∠KD

−− EF �

−− PK ,

−− DE �

−− RP

3

Which of the following can be used to prove that �ABD and �CBE are congruent?

A ASAB AASC SASD SSS

4 If �PQR and �FGH are congruent, which of the following must be a true statement?

F ∠PRQ � ∠GFHG

−−− QR �

−− GF

H ∠QRP � ∠GHF

J PQ _ PR

� GF _ GH

2 In the diagram below, −−

AB � −−

YW and

−− AC �

−− YX .

Which additional fact proves that �ABC and �YWX are congruent?

F −−

CB � −−−

XW G

−− CB �

−− XY

H ∠CAB � ∠WXYJ ∠ABC � ∠YWX

5 Triangles ABD and CBD share side

−− BD , and

−− AD �

−− CD . Which of the

following is sufficient to prove that �ABD and �CBD are congruent?

A ∠ABD � ∠CBDB ∠ADB � ∠CDBC BD � ADD ∠DAB � ∠BDC

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1 Triangles ABC and PQR are congruent.

52°

12

What is the measure of ∠PRQ?

A 38°B 48°C 52°D 90°

2 Triangle DEF is congruent to triangle XYZ.

710

16

What is the area of �XYZ?

F 35 square unitsG 56 square unitsH 80 square unitsJ 112 square units

3 Circle A is congruent to circle B.

12 in.

What is the circumference of circle B?

A 12π in.B 24π in.C 36π in.D 144π in.

4 Rectangle ABCD and rectangle PQRS are congruent.

Area = 864 m

24 m

2

What is the length of −−

AB ?

F 24 mG 36 mH 72 mJ 864 m

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1 In the figure below, �ABC is inscribed in circle T and m � AB = 50°.

50°

What is the m∠BAC?

A 25°B 40°C 55°D 65°

2 The center of the circle is P and m � MQN = 248°.

What is the m∠MPN?

F 56°G 112°H 124°J 248°

3 The center of this circle is O.

46°

What is the m∠TOR?

A 23°B 44°C 46°D 92°

4 In the circle, K is the center, m∠J = 30°, and �HJK is isosceles.

What is m � HJ ?

F 15°G 30°H 120°J 180°

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1 The center of the circle is B, −−

CD is a tangent to the circle at C, and m∠D = 25°.

What is the m∠ABC?

A 65° C 115°B 90° D 125°

2 Secants � � KD and � � LC intersect at point X.

n

4

5

6

What is the value of n?

AB · AC = AD · AE

F 3 H 7.5G 4.8 J 8

3 −− KL and

−− HJ intersect at M. What is the

length of −−−

HM ?

6

6

9

A 3 C 12B 4 D 36

4 Secants � � QS and � � RT intersect at point P, m � RQ = 63°, and m � ST = 81°. What is m∠QPT ?

63° 81°

F 18° H 72°G 36° J 108°

AE · EC = BE · ED

· = ·

m∠AEB = 1 _ 2 (m � AB + m � CD )

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11_36_OK_EOI_PbyO_894014.indd 25 6/24/09 10:18:14 AM

2 A new bike path is being built to go through a forest. The figure below shows the old path and the new path.

8 miles 15 miles

OLD BIKE PATH

NEW BIKE PATH

How many miles longer is the new path than the old path?

F 6 miG 7 miH 17 miJ 23 mi

3 Four students were asked to draw a right triangle and measure its sides. Which measurements can not be the sides for a correct drawing?

A 3 in., 4 in., 5 in.B 5 in., 12 in., 15 in.C 8 cm, 15 cm, 17 cmD 20 mm, 21 mm, 29 mm

4 Which set of measurements could be the lengths for the three sides of an acute triangle?

F 6 m, 8 m, 10 mG 6 ft, 9 ft, 12 ftH 4 mm, 9 mm, 10 mmJ 8 cm, 10 cm, 11 cm

1

x

2227

What is the value of x in right triangle ABC?

A 5B 7 √ � 5 C √ �� 1213 D 49

5

x

3x


AB ?

A 2xB x √ � 3 C 4xD x √ �� 10

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1

x

8 8

What is the value of x in the right triangle above?

A 4 √ � 2 B 8 √ � 2 C 16D 64

2 The hypotenuse of a 45-45-90 triangle is 26 √ � 2 inches. What is the length of each of the other two sides?

F 13 in. H 13 √ � 3 in.G 13

√ � 2 in. J 26 in.

4

a

b

c

30°

If b = 15 mm in the right triangle, what is the value of c?

F 5 √ � 3 mmG 10 √ � 3 mmH 15 √ � 3 mmJ 30 mm

3

a

bc

60°

If a = 12 in the figure above, what is the value of c?

A 6B 6 √ � 3 C 12 √ � 3 D 24

5 Quadrilateral ABCD is a trapezoid with

−− BC ‖

−− AD .

30° 45°

15

If the height of trapezoid ABCD is 10 units, which of the following is an expression for the perimeter of ABCD?

A 60 + 10 √ � 3 + 10 √ � 2 B 70 + 10 √ � 2 C 50 + 20 √ � 3 + 10 √ � 2 D 60 + 10 √ � 3 + 5 √ � 2

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1 In the right triangle, sin x = 8 _ 17

.

x

Which ratio is equal to cos x?

A 8 _ 15

B 15 _ 17

C 15 _ 8

D 17 _ 15

4 Akikta is standing 950 feet from the base of the Chase Tower in Oklahoma City.

28°

How tall to the nearest foot is the Chase Tower if he measures the angle of elevation from the ground to the building to be about 28°?

cos 28° = 0.88

sin 28° = 0.47

tan 28° = 0.53

F 428 ftG 504 ftH 846 ftJ 1,792 ft

3 In right triangle KML, m∠K = 41° and MK = 18. Which equation could be used to find the value of LM?

A LM = 18 sin 41°B LM = 18 cos 41°C LM = 18 tan 41°

D LM = 18 _ sin 41°

2 In the figure below, m∠B = 53°.

12


AB to the nearest tenth?

cos 53° ≈ 0.60

sin 53° ≈ 0.80

tan 53 ≈ 1.33

F 9.0G 9.6H 15.0J 20.0

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11_36_OK_EOI_PbyO_894014.indd 2811_36_OK_EOI_PbyO_894014.indd 28 6/17/10 4:11:20 PM6/17/10 4:11:20 PM

2

Which type of polyhedron is shown?

F rectangular prismG pentagonal pyramidH cubeJ square prism

4 Which of the following figures represents a hexagonal pyamid?

F

G

H

J

1 In the 1930’s there was an oil derrick on the grounds of the Oklahoma state capital. The derrick was in the shape of a square-based pyramid.How many vertices would a square- based pyramid have?

A 4B 5C 8D 12

5 Which figure has more edges?

A cubeB octagonal pyramidC triangular prismD pentagonal prism

3 Which of the following types of polyhedrons has the most number of faces?

A cubeB pentahedronC octagonal prismD decagonal pyramid

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1 A shipping box is in the shape of a triangular prism as shown.

12 cm

6 cm8 cm

How many square centimeters of cardboard are required to make this box, disregarding any overlapping?

SA = 2 ( bh _ 2 ) + ph

A 48 cm 2 B 216 cm 2 C 288 cm 2 D 336 cm 2

37.8 in.

4.9 in.

What is the volume of the cone, to the nearest tenth of a cubic inch? (use 3.14 for π.)

V = 1 _ 3 π r 2 h

A 178.1 cu in.B 196.0 cu in.C 294.2 cu in.D 588.4 cu in.

2 A circular cylinder has an altitude h and a base with radius r. Which of the following cylinders has the greatest volume?

V = π r 2 h

F r = 3 and h = 15G r = 6 and h = 15H r = 9 and h = 5J r = 9 and h = 15

4 The volume of a pyramid is 450 cubic centimeters. The area of the base is 45 square centimeters. Which of the following is the height of the pyramid?

V = 1 _ 3 Bh

F 10 cmG 20 cmH 25 cmJ 30 cm

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1 The large cone and small cone, shown in the figure below, are similar solids.

624

8

What is the radius of the small cone?

A 2B 3C 4D 6

2

4 cm

9 cm

What is the ratio of the surface areas for these two similar rectangular prisms?

SA = ph + B

F 3 to 2G 9 to 4H 81 to 16J 729 to 64

4

10 cm

8 cm

If the diameter and height of the cylinder were multiplied by 4, what would be the total surface area of the new cylinder?

SA = 2π r 2 + 2πrh

F 224π cm 2 G 448π cm 2 H 1,344π cm 2 J 1,792π cm 2

3 The ratio of the side lengths for 2 cubes is 1 to 2. If the volume of the smaller cube is 30 cubic inches, what is the volume of the larger cube?

V = s 3

A 60 cu in.B 120 cu in.C 180 cu in.D 240 cu in.

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2 Two different drink cups are in the shapes of congruent cones. The base of one cup has an area of 9π square inches. The second cup has a slant height of 5 inches. What is the volume of each cup?

V = 1 _ 3 π r 2 h

F 12π cu in.G 15π cu in.H 25π cu in.J 36π cu in.

3 A brand name can of green beans is congruent to a can of a generic brand. If the generic brand can has a height of 14 centimeters and a radius of 4 centimeters, what is the area of the label on the name brand can?

(Use π = 22 _ 7 .)

LA = 2πrh

A 224 square centimetersB 352 square centimetersC 704 square centimetersD 1,408 square centimeters

4 Two congruent cubical boxes are used for shipping books. Each side of the first box has a length of 15 inches. What is the volume of the second box?

V = s 3

F 15 cubic inchesG 225 cubic inchesH 1,350 cubic inchesJ 3,375 cubic inches

1 Two different makes of softballs are congruent. The diameter of one is 4.5 inches. What is the surface area of the second ball to the nearest tenth of an inch?

(Use 3.14 for π.)

SA = 4π r 2

A 28.3 square inchesB 56.5 square inchesC 63.6 square inchesD 254.3 square inches

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1 The BOK Tower in Tulsa is the tallest building in Oklahoma. Tomas has cut out this cardboard net to form a model of the tower.

Which polyhedron is formed by the folded net?

A square pyramidB cubeC rectangular prismD triangular prism

2 The net below can be folded into a polyhedron.

What kind of polyhedron is the folded net?

F square pyramidG cubeH rectangular prismJ triangular prism

3 Shown below are three views of a 3-dimensional shape.

Which solid matches the top, front, and side views shown?

A

Front Side

B

Front Side

C

FrontSide

D

Front Side

4 The net for a hexagonal pyramid would be composed of which set of figures?

F 2 hexagons and 6 rectanglesG 1 hexagon and 6 trianglesH 6 hexagons and 1 triangleJ 1 hexagon and 5 triangles

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1 Lines g and h are parallel. If line g contains points (2, 5) and (-3, 1), what is the slope of line h?

A -6

B - 4 _ 5

C 4 _ 5

D 5 _ 4

2 The line shown below passes through (0, 6) and (1, 4).

y

x

What is the slope of a line perpendicular to the one shown?

F -2

G - 1 _ 2

H 1 _ 2

J 2

3 Segment AB is a diameter of circle O. If the coordinates of the center of the circle are (3, 2) and the coordinates of A are (1, -1), then what are the coordinates of point B?

Midpoint between two points

P 1 ( x 1 , y 1 ) and P 2 ( x 2 , y 2 ):

( x 1 + x 2 _ 2 ,

y 1 + y 2 _ 2 )

A (2, 1 _ 2 )

B (5, 5)

C (-1, -4)

D (6, 4)

4 What is the distance between points M(2, 6) and N(3, 1)?

Distance between two points

P 1 ( x 1 , y 1 ) and P 2 ( x 2 , y 2 ):

√ �� ( x 2 - x 1 ) 2 + ( y 2 - y 1 )

2

F √ �� 24

G √ �� 26

H √ �� 50

J √ �� 74

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1 Points A (-1, -2) , B (5, -2) and C (2, 2) are plotted and connected on the graph below.

y

x

What type of triangle is formed by the points A, B, and C ?

A equilateralB scaleneC rightD isosceles

2 Which set of points will form a right triangle?

F (0, 5) , (0, 0) , and (2, 2) G (-3, 1) , (-1, 4) , and (3, 0) H (0, -4) , (1, 4) , and (4, -2) J (0, 0) , (2, 3) , and (5, 4)

3 Three vertices and two sides of parallelogram DEFG are shown on the graph.

y

x

What are the coordinates for point F that would complete the parallelogram?

A (6, 5) B (4, 4) C (-8, 3) D (5, 5)

4 Minya places a map of the Tulsa region on a coordinate plane with Tulsa at the origin. Four cities to the east of Tulsa have the following coordinates on her map: Claremore (2, 1), Colcord (5, 1), Stilwell (5, -3), and Haskel (2, -3). Which would be the most specific name for the quadrilateral determined by these four cities?

F parallelogramG squareH rectangleJ kiteC

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4 The vertices of parallelogram ABCDare A(-3, 0), B(-1, 3), C(-1, -2), and D(-3, -5). If the figure is translated 4 units to the right and 2 units up, what are the coordinates of vertex B′?

F (-3, -1)G (-5, 1)H (1, 7)J (3, 5)

1 Triangle JKL is graphed on the coordinate plane as shown below.

y

x

If �JKL is rotated 180° about the origin, what are the coordinates of J′?

A (5, 3) B (3, 0) C (3, 5) D (3, -5)

2 The vertices of �ABC are A(0, 6), B(2, 1), and C (-3, 4). If the figure is reflected across the x-axis to create �WXY, what would be the coordinates of the vertices for �WXY ?

F W (-6, 0) , X (2, 1) , Y (-3, -4) G W (-3, -4) , X (2, 1) , Y (0, -6) H W (0, -6) , X (2, -1) , Y (-3, -4) J W (0, 6) , X (-2, 1) , Y (3, -4)

3 Triangle HJK below is translated so that the coordinates of the new vertices are H′(-2, 4), J′(1, 4), and K′(2, 0).

y

x

What statement describes this transformation?

A (x, y) → (x + 1, y + 2)B (x, y) → (x + 1, y - 2)C (x, y) → (x - 1, y + 2)D (x, y) → (x - 2, y + 1)

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Record your answers by coloring in the appropriate bubble for the best answer to each question.

1 A B C D

2 F G H J

3 A B C D

4 F G H J

5 A B C D

6 F G H J

7 A B C D

8 F G H J

9 A B C D

10 F G H J

11 A B C D

12 F G H J

13 A B C D

14 F G H J

15 A B C D

16 F G H J

17 A B C D

18 F G H J

19 A B C D

20 F G H J

21 A B C D

22 F G H J

23 A B C D

24 F G H J

25 A B C D

26 F G H J

27 A B C D

28 F G H J

29 A B C D

30 F G H J

31 A B C D

32 F G H J

33 A B C D

34 F G H J

35 A B C D

36 F G H J

37 A B C D

38 F G H J

39 A B C D

40 F G H J

41 A B C D

42 F G H J

43 A B C D

44 F G H J

45 A B C D

46 F G H J

47 A B C D

48 F G H J

49 A B C D

50 F G H J

51 A B C D

52 F G H J

53 A B C D

54 F G H J

55 A B C D

56 F G H J

57 A B C D

58 F G H J

59 A B C D

60 F G H J

61 A B C D

62 F G H J

63 A B C D

64 F G H J

65 A B C D

66 F G H J

67 A B C D

68 F G H J

69 A B C D

70 F G H J

71 A B C D

72 F G H J

73 A B C D

74 F G H J

75 A B C D

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Practice TestStudent Answer Document

Name Date


37_OK_EOI_SAD_894014.indd 37 6/3/09 12:32:26 PM

7/3/09 1:44:00 PM038_OK_EOI_SAD_894014 038

31

4 Transversal t cuts parallel lines a and b.

a b

t1

2

54

What is m∠4 if m∠1 = 80°?

F 10°G 80°H 90°J 100°

Which of the following can serve as a counterexample to the assertion that two lines that are not parallel always intersect?

A intersecting linesB parallel linesC perpendicular linesD skew lines

If a and b are both negative numbers, which of the following expressions must also be negative?

A a _ b

B a + bC a - b

D 3ab

2 The net of a cylinder is shown below as two congruent circles and a square.

If the radius of the circles is 1 cm, then what is the surface area to the nearest tenth of a square centimeter? (Use π ≈ 3.14.)

SA = 2π r 2 + 2πrh

F 16.2 cm 2 G 18.8 cm 2 H 45.8 cm 2 J 59.2 cm 2

5 Which of the following is another name for a regular triangle?

A an obtuse triangleB a right triangleC an equilateral triangleD a scalene triangle

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Practice Test

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39_56_OK_EOI_PT_894014.indd 39 6/26/09 1:31:24 PM

6 A pentagonal prism has how many faces?

F 5G 7H 10J 15

10 Trey placed a rectangular box in an empty cylindrical can.

10 in.

30 in.

24 in.

6 in.

8 in.

What is the volume of the empty space in the can to the nearest cubic inch? (Use 3.14 for π.)

V (cylinder) = π r 2 h

V (rectangular prism) = �wh

F 3,840 in 3 G 13,085 in 3 H 16,800 in 3 J 53,779 in 3

11 What is the measure of each exterior angle of a regular octagon?

A 8°B 45°C 135°D 1080°

7 A triangle has a base 12 inches long and an area of 36 square inches. What is the length of the altitude to the base side?

A 3 in. C 5 in.B 4 in. D 6 in.

9 The hypotenuse of a 30°-60°-90° right triangle measures 30 inches. What is the length of the side opposite the 60° angle?

A 10 √ � 3 in.B 15 in.C 15 √ � 2 in.D 15 √ � 3 in.

8 The diagonals of a rhombus are perpendicular. If the slope of onediagonal is - 3 _

2 , what is the slope of

the other diagonal?

F -1 H 2 _ 3

G - 3 _ 2 J 3 _

2

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GO ON

Practice Test (continued)

39_56_OK_EOI_PT_894014.indd 40 6/30/09 11:57:55 AM

12 Triangles ABC and DEC are similar with AD = 6, DC = 12, AB = 6, and BE = 4.

What is the perimeter of �DCE?

F 24G 28H 32J 36

14 A truck tire has a diameter of 3 feet. How far will the truck travel with 20 rotations of the tire?

C = 2πr

F 30π ftG 60π ftH 120π ftJ 180π ft

15

24 ft

x

h

What is the height of the flagpole shown above to the nearest tenth of a foot?

cos x ≈ 0.55sin x ≈ 0.83tan x ≈ 1.50

A 16.0 ftB 19.9 ftC 29.7 ftD 36.0 ft

13 All rectangles are parallelograms.

Which of the following is the conditional form of the above statement?

A If a figure is a parallelogram, then it is a rectangle.

B If a figure is a rectangle, then it is a parallelogram.

C A figure is a parallelogram if and only if it is a rectangle.

D If a figure has 4 sides, then it is both a rectangle and a parallelogram.

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17

16 y

x

If triangle EFG is rotated 270° clockwise about the origin, what are the coordinates of G′?

F (-2, 4) G (-2, -4) H (-4, 2) J (2, -4)

18 A conical pile of sand has a height of 5 meters and a diameter of 12 meters. How many cubic meters of sand are in the pile?

V = 1 _ 3 π r 2 h

F 20π cubic metersG 50π cubic metersH 60π cubic metersJ 240π cubic meters

Point G is the midpoint of −−

FH . Given F (-2, 3) and G(1, 4), what are the coordinates of point H?

Midpoint between 2 points P 1 ( x 1 , y 1 ) and P 2 ( x 2 , y 2 ):

( x 1 + x 2 _ 2 ,

y 1 + y 2 _ 2 )

A (-0.5, 3.5) B (3.5, -0.5) C (4, 5) D (5, 4)

19 A rectangular prism has 12 edges. What is the maximum number of edges parallel to each other ?

A 12 edgesB 8 edgesC 4 edgesD 2 edges

20

35

1237

Which ratio represents cos P?

F 12 _ 35

H 35 _ 37

G 12 _ 37

J 35 _ 12

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39_56_OK_EOI_PT_894014.indd 42 6/26/09 3:42:06 PM

2321 Which of the following could be the lengths of the three sides of a right triangle?

A 11, 11, and 22B √ � 3 , √ � 5 , and 8C 2, 4, and √ �� 10 D √ � 3 , √ � 5 , and √ � 8

“A triangle cannot have an obtuse angle.”

Which of the following could provide a counterexample to the above statement?

A scalene triangleB right triangleC equilateral triangleD acute triangle

24 Quadrilateral LMNP is a parallelogram.

y

x

What are the coordinates for the midpoint of either diagonal?

Midpoint between two points P 1 ( x 1 , y 1 ) and P 2 ( x 2 , y 2 ):

( x 1 + x 2 _ 2 ,

y 1 + y 2 _ 2 )

F (6, 4) G (3, 2) H (2.5, 2) J (2.5, 0)

22 In the circle, m � BD = 24°, m∠BAD = 32°, secants � � BC and � � DE intersect at point A.

What is m � CE ?

m∠QPS = 1 _ 2 (m � RT - m � QS )

F 4° G 40°H 68°J 88°

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25 In the figure, −−

AE bisects −−

BD .

1

2 34 5

6

Which of the following is not sufficient to prove that �ABC and �EDC are congruent?

A −−

AC � −−

CE B ∠2 � ∠5C

−− AB ‖

−− DE

D ∠1 � ∠2

26 The hypotenuse of a right triangle has a length of 8 and one leg has a length of 5. What is the exact length of the other leg?

F 3 G √ �� 13 H √ �� 39 J √ �� 89

27 If the sum of the measures of two angles equals 90°, then the two angles are complementary. If m∠A = 20° and m∠B = 70°, which of the following is a logical conclusion?

A m∠A + m∠B = m∠CB ∠A and ∠B are interior angles of a

triangle.C ∠A and ∠B are vertical angles.D ∠A and ∠B are complementary.

28 Line a cuts across lines b and c.

a

b c

(2x + 17)°(3x)°

For what value of x will lines b and c be parallel?

F 3.4 G 17 H 32.6J 51

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29 Triangle ABC is a right triangle and AC = 8.

x

x

8

What is the exact value of x?

A √ � 2 B 4 √ � 2 C 16 √ � 2 D 8

30 Triangle ABC is to be translated to �A′B′C′ by using the following rule. (x, y) → (x - 2, y + 3)

y

x

What will be the coordinates of point B′?

F (-3, 5) G (2, 0) H (1, 5) J (2, 0)

31 Point C is the center of the circle, and m∠CAB = 25°.

What is m � ADB ?

A 25° B 100° C 130°D 230°

32 In right triangle DEF, e = 4 √ � 3 and m∠D = 30°.

30°e

df

What is the value of f?

F 8 G 12 H 8 √ � 3 J 16

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39_56_OK_EOI_PT_894014.indd 45 6/26/09 1:31:44 PM

33 Quadrilateral WXYZ is a kite.

8"

14" 26"


ZY ?

A 14 in. B 16 in. C 26 in.D 29.5 in.

36 Each face on a cubical block of ice has an area of 81 square inches. A salt block is in the shape of a cube congruent to the block of ice. What is the volume of the salt block?

V = s 3

F 9 in 3 G 27 in 3 H 81 in 3 J 729 in 3


DE ‖ −−

AC .

Which could be used to prove that �ABC is similar to �DBE?

A ASA B SSA C AAD SSS

34 A kite is flying so that the string makes a 55° angle with the ground.

55°

400 fth

How high above the ground, to the nearest foot, is the kite if 400 feet of string has been released?

sin 55° ≈ 0.82cos 55° ≈ 0.57tan 55° ≈ 1.43

F 228 ft H 488 ftG 328 ft J 572 ft

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37 The base of a pyramid is a square.

5 cm

6 cm

What is the volume of the pyramid?

V = 1 _ 3 Bh

A 10 cm 3 B 30 cm 3 C 50 cm 3 D 150 cm 3

38

2

1

What is the degree measure of ∠2 if m∠1 = (3x + 9)° and m∠2 = (5x + 3)°?

F 18° G 21°H 72°J 108°

39 In a model of the solar system, Earth has a diameter of 15 inches and Mars has a diameter of 9 inches. What is the ratio of their surface areas?

A 5 to 3 B 25 to 9 C 125 to 27D 8 to 1

40 Chords −−

EF and −−

GH intersect at K, EK = 3, FK = 10, and HK = 12.

1012

3

What is the value of GK?

· = ·

F 1G 2.5H 4.5J 6

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39_56_OK_EOI_PT_894014.indd 47 6/29/09 9:58:42 AM

41

What type of polyhedron is shown above?

A pentagonal pyramidB pentagonal prismC hexagonal prismD octagonal pyramid

42 y

x

What is the distance between point H and point J?

Distance between two points P 1 ( x 1 , y 1 ) and P 2 ( x 2 , y 2 ):

√ �� ( x 2 - x 1 ) 2 + ( y 2 - y 1 )

2

F √ �� 50 G √ �� 34 H √ �� 32 J √ �� 10

43 Transversal p cuts parallel lines m and n.

1 2

657 8

43

m

p

n

Which of the following names all the angles that must be congruent to ∠7?

A ∠6, ∠4, ∠2B ∠8, ∠4C ∠5, ∠3, ∠1D ∠6, ∠3, ∠2

44 The net of a triangular prism is composed of which shapes?

F 3 rectangles and 2 trianglesG 2 rectangles and 3 trianglesH 4 rectangles and 2 trianglesJ 3 rectangles and 1 triangle

45 What type of triangle is formed by the points P(3, 4), Q(2, 1), and R(4, 1)?

A isosceles C scaleneB right D equilateral

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46 Triangle ABC is similar to �XYZ.

8

1016


XY ?

F 8 G 10 H 12.8J 20

47 In the right triangle, m∠Q = 17° and NP = 23.

17°23

x

Which equation could be used to find the value of x?

A x = 23 _ sin 17°

B x = 23 _ cos 17°

C x = tan 17° _

23

D x = 23 tan 17°

48 The measure of two complementary angles are given by (2x - 7)° and (5x - 1)°. What is the measure of the larger angle?

F 14° G 21° H 69°J 133°

49 If B is between A and C, then AB + BC = AC.

Which of the following is the inverse of this statement?

A If B is not between A and C, then AB + BC ≠ AC.

B If AB + BC = AC, then B is between A and C.

C If AB + BC ≠ AC, then B is not between A and C.

D If B is not between A and C, then AB ≠ BC.

50 Which could be the measurements for the three sides of an obtuse triangle?

F 8 m, 12 m, 17 mG 21 cm, 28 cm, 35 cmH √ � 7 ft, 8 ft, √ �� 71 ftJ 20 in., 20 in., 26 in.

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39_56_OK_EOI_PT_894014.indd 49 6/26/09 1:31:57 PM

52 In the figure, line � is the perpendicular bisector of

−− AB

and −−

AP � −−

BP . Suppose Q is another point on �.

�

Which is a reasonable conjecture about this situation?

F −−−

AQ � −−

AP G

−−− BQ �

−− BP

H −−−

AQ � −−−

BQ J ∠APB � ∠AQB

53 In circle O, −−

AB is a diameter, −−

CB is achord, and m � BC = 120°.

What is the measure of ∠ABC?

A 15° B 30° C 60°D 120°


BD is perpendicular to

−− AC .

2012

15


AC ?

F 9 G 25 H 42.5J 59

51 In the figure below, −−

BC � −−

DC and

−− AC �

−− EC .

What theorem or postulate can be used to prove �ABC � �EDC?

A AAA B SSS C SASD AAS

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55

a

b

c45°

If a = 2 √ � 2 , then what is the value of c?

A 2 B 2 √ � 2 C 4D 4 √ � 2

56 The top of a swimming pool is congruent to the circle at midcourt of a basketball court. If the midcourt circle has a radius of 6 feet, what is the circumference of the top of the swimming pool to the nearest tenth of a foot? (Use 3.14 for π.)

F 12.0 ft G 18.8 ft H 37.7 ftJ 113.0 ft

57 What is the slope of a line parallel to the line through (-4, -2) and (-1, 2)?

A - 4 _ 3 C 3 _

4

B - 3 _ 4 D 4 _

3

58

14

5 62 3

Which of the following would be sufficient to prove that �ABC and �DEF are similar?

F −−

AB � −−

DE G ∠1 � ∠6 H

−− BC �

−− EF

J ∠1 � ∠4

59

10 cm

8 cm

What is the surface area of this cylinder?

SA = 2π r 2 + 2πrh

A 96π cm 2 B 112π cm 2 C 160π cm 2 D 208π cm 2

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39_56_OK_EOI_PT_894014.indd 51 6/26/09 1:32:04 PM


RS is a radius, −−

ST is tangent to circle R at point S, and m∠RQS = 67°.

What is m∠QST?

F 23°G 46°H 67°J 113°

61 What is the most specific name for the quadrilateral represented by the points A(-3, -2), B(-2, 2), C(2, 1), and D(1, -3)?

A parallelogramB rectangleC rhombusD square

62 The lengths of two similar rectangles are in a ratio of 1:2. If the area of the smaller rectangle is 12 square centimeters, what is the area of the larger rectangle?

F 12 cm 2 G 24 cm 2 H 36 cm 2 J 48 cm 2

6316 cm

12 cm32 cm

A larger rectangular prism with a height of 40 centimeters is similar to the one above. What is the volume of the larger prism?

A 6,144 cm 3 B 15,360 cm 3 C 64,000 cm 3 D 96,000 cm 3

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64 ∠ACB is inscribed in circle P,m � AC = 70°, and m � CB = 160°.

What is the measure of ∠ACB?

F 35° G 65° H 80°J 130°

65 Consider the following two statements.

(1) If a set is finite, then any subset of the set is finite.

(2) The set of integers between -100 and 100 is finite.

Which statement below follows logically from statements (1) and (2)?

A The set of integers is finite.B The set of integers between -100

and 100 is not a subset of an infinite set.

C A subset of the set of integers between -100 and 100 is also finite.

D A subset of the set of integers between -100 and 100 is infinite.

66 The Ballerina is an 8 1 _ 2 -foot tall statue

on display in the lobby of the Oklahoma City Civic Center. It honors Oklahoma’s five American Indian ballerinas. If a spotlight is placed 4 feet perpendicular from its base, which ratio can be used to determine the angle of elevation, θ, to aim the light directly at the top of the statue?

F sin θ = 4 _ 8.5

G cos θ = 4 _ 8.5

H tan θ = 4 _ 8.5

J tan θ = 8.5 _ 4

67 A cone with a radius of 3 units is similar to a cone with a radius of 6 units. How many times greater is the volume of the larger cone than the volume of the smaller cone?

A 2B 4C 8D 216

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39_56_OK_EOI_PT_894014.indd 53 6/26/09 1:32:09 PM

68 Quadrilateral WXYZ is a square and XZ = 14 centimeters.

What is the perimeter of WXYZ?

F 28 √ � 2 cm G 28 cmH 7 √ � 2 cmJ 7 cm

69 Right triangles MNP and QRS are congruent.

517

12

What is the area of �QRS?

A 30 square unitsB 42.5 square unitsC 60 square unitsD 102 square units

70

This figure is a net of which solid?

F triangular-based pyramidG triangular prismH coneJ rectangular prism

71 A cable is attached to a young tree to keep it perpendicular to the ground. The cable is attached to the tree 15 feet above the ground and tied to a stake that is placed 8 feet from the base of the tree. If an extra 2 feet of cable is needed to fasten the cable to the tree and the stake, then what is the minimum length of cable that is needed?

A 14.7 ft B 17 ftC 19 ftD 25 ft

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AB � −−

AC .

4

5 6

1

32

Which of the following could be used to prove that �ABD and �ACD are congruent?

F D is the midpoint of −−

BC .G �ABC is isosceles.H ∠1 � ∠5J m∠3 + m∠5 = 180°

73 Maria and Kelly have glasses that are congruent cylinders 10 centimeters in diameter. If the volume of Maria’s glass is 375π cubic centimeters, what is the height of Kelly’s glass?

V = π r 2 h

A 3.75 cm B 15 cmC 37.5 cmD 75 cm

74 Triangle QRS is isosceles.

x90°

16


F 32 H 8G 16 √ � 2 J 8 √ � 2

75 A 20-foot water slide at a local water park makes a 32° angle with the ground.

32°

20 ft

What is the length of the ladder to the nearest tenth of a foot?

sin 32° ≈ 0.53cos 32° ≈ 0.85tan 32° ≈ 0.62

A 10.6 ft C 23.6 ftB 12.4 ft D 32.0 ft

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Mastering the EOI, Geometry, SE - Glencoe