VIRGINIA STANDARDS OF LEARNINGSpring 2006 Released Test

END OF COURSEGEOMETRYCORE 1

Property of the Virginia Department of Education2007 by the Commonwealth of Virginia, Department of Education, P.O. Box 2120, Richmond, Virginia 23218-2120.All rights reserved. Except as permitted by law, this material may not be reproduced or used in any form or by anymeans, electronic or mechanical, including photocopying or recording, or by any information storage or retrieval system,without written permission from the copyright owner. Commonwealth of Virginia public school educators mayreproduce any portion of these released tests for noncommercial educational purposes without requesting permission.All others should direct their written requests to the Virginia Department of Education, Division of Assessment andReporting, at the above address or by e-mail to darfax@doe.virginia.gov.

Geometry Formula SheetGeometric Formulasb1hh

h

12

bh

12

A=

l

B

b2

b

A=

h

V = BhL.A. = hpS.A.= L.A. + 2B

h(b1 + b2 )

V = 13 BhL.A.= 12 lpS.A.= L.A. + B

rw

r

r

h

l

43

A = lwp = 2(l + w)bl

hh

A = bh

l

w

V = lwhS.A.= 2lw + 2lh + 2wh

13

Meaningangle A

m

measure of angle A

ExampleAB

Meaningvector ABright angle

AB

line segment AB

AB CD

AB

measure ofline segment AB

AB CD

AB

line AB

A

ABC

triangle ABC

A

ABCD

rectangle ABCD

ABCD

parallelogram ABCD

Copyright 2006 by the Commonwealth of Virginia Department of Education

c2

=

a2

+ b2

Abbreviations

Geometric SymbolsExampleA

b

r

b

A

c

a

h

Line AB is parallel toline CD.Line AB is perpendicularto line CD.B Angle A is congruent toangle B.B Triangle A is similar totriangle B.Similarly markedsegments are congruent.Similarly marked anglesare congruent.

VolumeLateral AreaTotal SurfaceAreaArea of Base

VL.A.S.A.B

Pi227

Geometry2

DIRECTIONS

Read and solve each question. Then mark thespace on your answer document for the bestanswer.

45

x

SAMPLE

A

D

Two parallel sections of pipe are joinedwith a connecting pipe as shown. Whatis the value of x?

E

90G 115H 135J 160F

B

C

If ABC is similar to ADE, thenAB : AD ? : AE. Which replaces the? to make the statement true?AC B AEC DED BCA

1

3

Parallel lines l and m are cut bytransversal t, m4 m5, andm6 m7.

B5

l

4

42867

C

At

Which of the following is the measureof the supplement of CAB?

What is the measure of 8?

42B 90C 132D 142A

120B 90C 65D 45A

3

m

4

6

What are the measures of twocomplementary angles if the differenceof their measures is 18?36,G 41,H 81,J 86,F

2

54499994

3

467

5

Line n intersects lines p, q, r, and s,forming the indicated angles.

130

58

Which will prove that line l is parallelto line m?2G 3H 5J 7F

40

1

O

O

50

O

35O

Which two lines are parallel?p and qB p and rC q and rD r and sA

4

7621

7

9

2

3

541

3( -1, 2) Q

-5 -4 -3 -2 -1

21O

-1-2-3-4-5

1

2

3

4

5

R (1, -2)4

For the construction shown above,which of the following arcs must bedrawn first?

Which two points determine a line

1B 2C 3D 4A

parallel to QR ?(1, 1) and (2, 1)B (1, 1) and (2, 3)C (1, 4) and (5, 2)D (2, 1) and (2, 1)A

8

Given: m1 110

1 23 4

5 67 8

y

z

Which must be true if y z?m8G m7H m6J m5F

10011080110

5

10

11

Which line is apparently perpendicular

to AB ?AB

Which segment is apparentlycongruent to AB?

C

AWG AXH AYJ AZF

D

6

PW

PX

PY

PZ

12

13

Car Features

AutomaticTransmission

Which set of statements represents aninvalid argument?A

If I work, then I will make money.If I make money, then I will buy clothes.If I work, then I will buy clothes.

B

If we pass Geometry, then we will playsports.If we play sports, then we will get atrophy.If we do not get a trophy, then we didnot pass Geometry.

C

If Mark goes camping, then he will gofishing.If Mark goes fishing, then he will buybait.If Mark does not buy bait, then he willgo camping.

D

If it is your birthday, then you willget ice cream.If you get ice cream, then you willget cake.If it is your birthday, then you willget cake.

Rear-WheelDrive

4-CylinderEngine

According to the Venn diagram above,which is true?All cars have automatic transmissionsand rear-wheel drive.G No cars have 4 cylinders and rear-wheeldrive.H All cars have rear-wheel drive.J Some cars have automatic transmissionsand 4 cylinders.F

7

14

X

16

Triangles ABC and EFG are similarwith measurements in centimeters asshown.

L

M

GY

C7

If triangle XYZ is similar to triangleXLM, then

9

A 5

B

E

10

XM : XZ XL : XYG XM : XZ XY : XLH XL : LM YZ : XZJ XL : LY XZ : MZF

F

What is the perimeter of triangle EFG?21G 24H 36J 42F

Z

cmcmcmcm17

Given: ABCD is a parallelogram.

A15

B

Which is the contrapositive of thestatement below?If you do your homework, then youwill be prepared for the test.

D

If you are prepared for the test, thenyou did your homework.B If you are not prepared for the test, thenyou did not do your homework.C If you do your homework, then you willbe prepared for the test.D If you do not do your homework, thenyou will not be prepared for the test.A

C

Prove: ABD CDBA C

Opposite angles of aparallelogram are congruent.

AD BC

Opposite sides of aparallelogram are congruent.

AB CD

Opposite sides of aparallelogram are congruent.

Therefore, ABD CDB by whichpostulate/theorem?SSAB ASAC SASD AASA

8

18

19

Three boys are in a field flying kites.Viewed from above, the angle at Kyle,K, measures 45, and the angle at Jake,J, measures 65.

X

52

Y

65

52

50

Z

Using the information in the drawing,which angle has the least measure?

45

XZYB XYZC ZXYD YZXA

Which shows the distances betweenthe boys in order from least togreatest?LJ, JK, KLG KL, KJ, LJH KJ, LK, JLJ LJ, LK, JKF

20

Which of the following could not be thelengths of the sides of a triangle?8 in., 19 in., 15 in.G 6 in., 3 in., 9 in.H 4 in., 5 in., 6 in.J 10 in., 8 in., 9 in.F

9

21

22

Scotty is making a train of dominoeson the floor.

75

10

Do

mi

no

A fire truck has a ladder that canextend to 60 feet in length. The laddercan be safely raised to a maximumangle of 75 with the horizontal.Disregarding the height of the firetruck itself, which is closest to themaximum height that the ladder cansafely reach?

8 DominoesHow many dominoes are needed tocomplete the triangle?

sin 75 0.966cos 75 0.259tan 75 3.7315.53B 57.96C 60.00D 62.12A

es

6G 12H 18J 36F

ftftftft

10

23

Using the measures shown, whichtriangle must be a right triangle?

24

The spokes on a wagon wheel formtwelve congruent central angles.

A

7 cm

A

W

N

A

O

4 cm

C

8 cm

B

GD

What is the degree measure of WG?B

5 in.

E

H

C

30G 90H 120J 150F

6 in.

F

3 in.

G

3 ft

2 ft4 ft

I

LD

12 m

J5m

13 mK

11

25

26

XYZW is a rectangle.

X

In the drawing, a regular polygon ispartially covered by a rectangle.

Y

135

W

Z

Which of the following is notnecessarily true?XY WZB YZ WZC XZ WYD XY XWA

What is the number of sides of thispolygon?12G 10H 8J 6F

12

27

29

D

AC

E

O

B

A

45

B

C

If E C, what is mE?110B 120C 135D 150A

If mAOB 45 in circle O, what ismACB?22.5B 45C 67.5D 90A

28

Three vertices of a parallelogram havecoordinates (1, 4), (3, 8), and (5, 0).

y9876543219 8 7 6 5 4 3 2 1 012

1

2

3

4

5

6

7

8

9

x

3456789

What are the coordinates of thesecond-quadrant vertex?(3, 12)G (1, 4)H (1, 4)J (9, 4)F

13

30

Chords AB and CD intersect, formingsegments with the measures shown.

32

In the rectangle PQRS, m1 50.

P

Q

C

21

A

4

S

3x

R

What is m2?

O

B

6

130G 85H 70J 65F

DWhat is the value of x?5G 8H 10J 24F

31

33

A regular pentagon and a regularhexagon share a side as shown inthe figure.

D

IC

A

G

360 mACB 240 mACC 180 mACD 120

HF

B

The sum of mAB and mBC is equalto

E

A

What is the measure of ABG?108B 120C 132D 144A

14

34

A swimming pool is being filled at therate of 12 cubic yards per minute. Ifthe pool is 18 yards long, 10 yardswide, and 3 yards deep, how manyminutes will it take to fill the pool?

36

45 minutesG 101 minutesH 540 minutesJ 1,233 minutes

Which of the following nets can befolded along the dashed lines to forma cube?

F

F

G

35

This drawing shows cubic boxesstacked in the corner of a warehouse.

H

J

If each box will hold 8 cubic feet, whatis the total capacity of the stack ofboxes?488B 496C 504D 512A

cubiccubiccubiccubic

feetfeetfeetfeet

15

37

A machine for baling hay produces

38

cylindrical bales that are 6 feet in1diameter and 5 feet in height.3

Which is closest to the number of cubicfeet in each bale of hay the machineproduces?

A boy knows that his height is 6 feet.At the time of day when his shadow is4 feet, a trees shadow is 24 feet.

64

100B 151C 301D 603

24

A

What is the height of the tree?36G 24H 18J 12F

16

ftftftft

39

The cylinders shown are similar.

y

40

B

5

8m

C

43

A

D

2

2m

15 4 3 2 1

01

1

2

3

4

5

x

2

14 m

345

If parallelogram ABCD is translated sothat the new location of point D is(1, 2), what would be the new locationof point B?

What is the volume of the largercylinder?

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

3

56 m3B 224 m3C 896 m3D 3,584 mA

17

41

Triangle ABC is a transformation oftriangle ABC.

4254

A

321

B

C

-5 -4 -3 -2 -1 O-1-2-3-4-5

l

PB'

C'

1

2

3

4

5

A'What is most likely the slope of the linegraphed above?

If A A, B B, and C C, ABC isa

F

reflection of triangle ABC across line lB 180 rotation of triangle ABC aboutPoint PC translation of triangle ABC across theline lD 90 rotation of triangle ABC across theline lA

G

18

112

H

12

J

1

y

43

*(1, 7)

+(7, 7)

)(1, 1)

,(7, 1)

44

l

m

xThe figure shown is apparentlysymmetric with respect to

What is the point of intersection of BDand AC?(3,B (3,C (4,D (4,A

line l onlyG line m onlyH both lines l and mJ neither line l nor line mF

3)4)4)3)

45

What is the midpoint of the segmentjoining (12, 2) and (5, 7)?(9, 17)B (5, 3)C (8.5, 4.5)D (3.5, 2.5)A

19

Answer Key - 2A27MTest SequenceNumber123456789101112131415161718192021222324252627282930313233343536373839404142434445

Correct AnswerCHBFBJAJAJAJCJBFCJCGBFDHDHCGAGCJAFBFBFDGAGCFD

ReportingCategory001001001001001001001001001001001002002002002002002002002002002002002003003003003003003003003003003004004004004004004005005005005005005

Reporting Category DescriptionLines and AnglesLines and AnglesLines and AnglesLines and AnglesLines and AnglesLines and AnglesLines and AnglesLines and AnglesLines and AnglesLines and AnglesLines and AnglesTriangles and LogicTriangles and LogicTriangles and LogicTriangles and LogicTriangles and LogicTriangles and LogicTriangles and LogicTriangles and LogicTriangles and LogicTriangles and LogicTriangles and LogicTriangles and LogicPolygons and CirclesPolygons and CirclesPolygons and CirclesPolygons and CirclesPolygons and CirclesPolygons and CirclesPolygons and CirclesPolygons and CirclesPolygons and CirclesPolygons and CirclesThree-Dimensional FiguresThree-Dimensional FiguresThree-Dimensional FiguresThree-Dimensional FiguresThree-Dimensional FiguresThree-Dimensional FiguresCoordinate Relations and TransformationsCoordinate Relations and TransformationsCoordinate Relations and TransformationsCoordinate Relations and TransformationsCoordinate Relations and TransformationsCoordinate Relations and Transformations

Geometry, Core 1If you get thismany itemscorrect:0123456789101112131415161718192021222324252627282930313233343536373839404142434445

Then yourconverted scalescore is:000183217239255267278287296303311317323329335341346351356362367371377382386392397401407412417423429435441448455463471481491504520541576600