X G U A - Quia a right circular cylinder and a right circular cone. cm Which is closest to the surface area of the contianer? a. 1175 cm² b. 1935 cm² c. 2315 cm² d. 1555 cm²

2014 Geometry Practice SOL version 1

Name:

____ 1. Let p represent:

Two angles are vertical angles.

Let q represent:

The angles are congruent.

What is the symbolic representation of the following statement?

If two angles are not congruent, then the angles are not vertical angles.

a. b. c. d.

____ 2. Tammie is drawing the

perpendicular bisector of .

Which point is on the

perpendicular bisector of ?

a. L b. S c. Y d. B

____ 3. In this figure, parallel lines b and n

are intersected by line k.

Which pair of angles is NOT

supplementary?

a. and b. and c. and d. and

____ 4. What type of construction

is illustrated in the figure?

a. The bisection of c. An angle congruent to

b. The bisection of d. A line segment congruent to

J W

L

S

Y

B

b

n

k

GX

U A


____ 5. The Venn diagram represents students

who play instruments in the orchestra.

Identify each region of the Venn

diagram that represents students who

play only the tuba and the clarinet.

a. 5, 6, 10 b. 6 c. none d. 5, 10

____ 6. An angle congruent to

angle T is being

constructed.

Which ray could be

drawn to construct an

angle congruent to ?

a.

b.

c.

d.

____ 7. Which is a valid conclusion that can be drawn from these statements?

If a quadrilateral is a rectangle, then it is a parallelogram.

If a quadrilateral is a parallelogram, then its opposite sides are congruent.

a. Every quadrilateral is a rectangle.

b. Every parallelogram is a rectangle.

c. Opposite sides of a rectangle are congruent.

d. Opposite sides of a quadrilateral are congruent.

____ 8. What is the inverse of the following statement?

If the measure of an angle is 90º, then it is a right angle.

a. If the measure of an angle is not 90º, then it is not a right angle.

b. If it is not a right angle, then the measure of an angle is not 90º.

c. If it is a right angle, then the measure of an angle is 90º.

d. If the measure of an angle is not 90º, then it is a right angle.

harp tuba

clarinet bass

T

S

X

VD

E


____ 9. Which diagram shows a pair of angle measures that prove lines q and l are parallel?

a.

c.

b.

d.

____ 10. This figure show parallel

stair railings through points

H, U, R, and F.

What is the value of x ?

a. 27 b. 45 c. 63 d. 117

11. Line d and m are cut by a transversal

What value of x proves that d // m ?

q l

z

r

123°

123°

q l

z

r

123°

57°

q l

z

r

123° 57°

q l

z

r

123°

123°

H U R F

63

d

m

141

(2x + 41)


____ 12. Given E (–3, 9) and T (7, –9)

What is the length of ?

a. b. c. d.

13. Line g contains the points

(–6, 7) and (6, –1).

Plot a point other than point S

with integral coordinates that

is on a line parallel to g and

passes through point S.

____ 14. Given : X(–9, –3) and E(–5, –1) What is the slope of ?

a. b.

c.

d.

E

T

1 2 3 4 5 6 7 8 9–1–2–3–4–5–6–7–8–9 x

1

2

3

4

5

6

7

8

9

–1

–2

–3

–4

–5

–6

–7

–8

–9

y

(3, –6)

Sg

1 2 3 4 5 6 7 8 9 10–1–2–3–4–5–6–7–8–9–10 x

1

2

3

4

5

6

7

8

9

10

–1

–2

–3

–4

–5

–6

–7

–8

–9

–10

y

2

1

2

1

2

2


____ 15. Which best describes

the construction in the

diagram shown?

a. The bisector of a line segment

b. A line segment congruent to a given line segment

c. A perpendicular to a given line at a point on the line

d. A perpendicular to a given line from a point not on the line

____ 16. Quadrilateral WSJC is shown.

If WSJC is reflected across the

line , what are the

coordinates of J’ ?

a. b. c. d.

____ 17. Given the measures shown in the diagram, which two triangles are congruent?

a. K and L b. R and M c. R and L d. K and M

B H

W

S

J

C

1 2 3 4 5 6 7 8 9–1–2–3–4–5–6–7–8–9 x

1

2

3

4

5

6

7

8

9

–1

–2

–3

–4

–5

–6

–7

–8

–9

y

KR

21

21

46

46

58

66

M L21

21

46 46

68

66


____ 18. The figure represents a ramp

with handrails.

Segments HJ and LM are

parallel to PQ.

Segments JK and MN are

parallel to QR.

Segments HP and JQ are

parallel to KR.

If , what is

?

a. 64º b. 90º c. 116º d. 154º

____ 19. For which polygon are both and lines of symmetry?

a.

c.

b.

d.

116

H J

K

LM

N

P Q

R


____ 20. Nori attached a wire

between two poles on a hill

as shown.

Which is closest to x, the

distance between the two

poles?

a. 48 yd b. 52 yd c. 114 yd d. 126 yd

____ 21. Triangles KRQ, KEQ, and FRQ

are show on the coordinate grid,

and all the vertices have

coordinates that are integers.

Which statement is true?

a. No two triangles are congruent.

b. Only and are congruent.

c. Only and are congruent.

d. Triangle KRQ, , and are all congruent

22. The lengths of two sides of a triangle are 22 feet and 49 feet. What is the range of possible lengths, in feet, for

the third side, x, of this triangle?

____ 23. Which of the following sets of lengths can represent the measures of the sides of a right triangle?

a. 4, 5, 6 b. 5, 7, 13 c. 8, 12, 17 d. 24, 32, 40

135

21

yd

K

R

F

E

Q

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y


____ 24. Part of a marching band formed by a triangle made with cornet players on one side, oboe players on one side,

and clarinet players on the third side.

• The angle formed by the cornet and clarinet players measured 47º

• The angle formed by the clarinet and oboe players measured 67º

Which orders the sides of this triangle from least to greatest using the instrument names?

a. oboe, cornet, clarinet c. cornet, clarinet, oboe

b. oboe, clarinet, cornet d. clarinet, cornet, oboe

____ 25. An equilateral triangle is folded in half.

What is x, the height of the equilateral

triangle?

a. yd b. 18 yd c. yd d. 9 yd

____ 26. Look at this triangle.

Which triangle is similar to the given triangle?

a.

c.

b.

d.

yd18

L

S

H

4 m

m

5.5 mm

5.5 mm

3 mm

4.13 mm4.13 mm2.25 mm 2.83 mm

3.77 mm

3 mm

5.83 mm

5.83 mm 4 mm

4 mm

5.5 mm


27. Click and drag each selected reason to the correct box

Given: Figure VJUZ with diagonal

;

Complete the proof of by selecting the

reasons for the last two statements.

Statements Reasons

Given

____ 28. A spectator is viewing the six cars

of a roller coaster as it travels down a

hill at an amusement park.

Which is the closest to the total

length of the six cars?

a. 14.4 ft b. 16.0 ft c. 25.0 ft d. 39.9 ft

29. Given: Parallelogram GDPL where

and .

What value of x proves this

parallelogram is a rhombus?

V

Z

J

U

24 ft

37

G

D

L

P

2x - 14

4x - 42


____ 30. Which could be the lengths of three sides of a triangle?

a. 16 cm, 10 cm, 6 cm c. 18 cm, 21 cm, 19 cm

b. 22 cm, 11 cm, 8 cm d. 30 cm, 18 cm, 11 cm

____ 31. Three triangles that do not overlap

are shown on the coordinate grid.

The coordinates of all vertices are

integers.

Which statement is true?

a. b. c. d.

____ 32. Using the information given,

which congruence postulate or

theorem can be used to prove

that ?

a. Hypotenuse-Leg Theorem c. Side-Angle-Side Postulate

b. Side-Side-Side Postulate d. Angle-Side-Angle Postulate

____ 33. Given: W lies on and U lies on

Which condition proves ?

a. c. b.

d.

F

Q

L

ZG1 2 3 4 5 6–1–2–3–4–5–6 x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

XW

AL

D

E

W

MU

Y


____ 34. The cross-section for a wooden beam

is modeled by the composite of

the regular pentagon and triangle

shown.

What is closest to the measure of

?

a. 158º b. 168º c. 163º d. 178º

____ 35. Given: Circle E with center at (–6, –5)

What equation could represent circle E?

a. c.

b. d.

____ 36. This container is composed

of a right circular cylinder and

a right circular cone.

Which is closest to the surface

area of the contianer?

a. 1175 cm² b. 1935 cm² c. 2315 cm² d. 1555 cm²

____ 37. A tablet computer box in the shape of a rectangular

prism is shown. The height of the box is 3 cm.

The height of the original box will be increased

by 2.5 centimeters so a new instruction manual

and an extra battery can be included. Which is

closest to the total surface area of the new box?

a. 515.5 in² b. 543 in² c. 567 in² d. 681 in²

S

Y

Q

12 cm

cm11

cm22

3 in

14 in

13.5in


____ 38. Given: Circle F

What is the value of y?

a. 39 b. 49 c. 88 d. 92

____ 39. Parallelogram GYWH is a

rhombus with

What is the ?

a. 35° b. 55° c. 110° d. 145°

____ 40. Circle L has a center at (–5, 6) and a diameter of 10 units. Which point lies on circle L?

a. (–9, 3) b. (–5, 6) c. (1, 14) d. (5, 16)

____ 41. This figure is composed of

an isosceles trapezoid and a

regular octagon.

What is the value of x ?

a. 103 b. 109 c. 116 d. 167

FB

A

K

T

49

92

G Y

WH

C

35

58 58


____ 42. An architect used this diagram to

design a curved balcony. She drew

a circle with a radius of 38 feet and a

central angle of 66° to determine the

length of railing needed for the

balcony.

Which is the closest to the length of

railing needed for the curved section

of the balcony?

a. 22 ft b. 44 ft c. 239 ft d. 832 ft

____ 43. A polygon is shown:

What is the measure

of ?

a. 64° b. 90° c. 116° d. 232°

____ 44. Given: Circle A

Which is the closest to the area

of the shaded sector of circle A

?

a. 26 mm² b. 143 mm² c. 238 mm² d. 380 mm²

45. The ratio of the lengths of the radii of two sphere is 4:7. What is the ratio of the volumes of these two spheres?

66

38

154

U Y

PF

TV

A

135

11mm

1 4 7 16 28 49 64 343


____ 46. The diagonals of rectangle USDX intersect

at the point (0, 4). One of the vertices

of the rectangle USDX is located at (–8,

8).

Which of the following could be the

location of another vertex of this

rectangle?

a. (8, 0) b. (–4, 6) c. (0, 8) d. (0, 0)

____ 47. A rectangular pyramid is shown.

What is the volume of the pyramid?

a. 2244 cm³ b. 1122 cm³ c. 748 cm³ d. 204 cm³

____ 48. A company is creating a new cylinderical container to replace its original cylindrical container.

• The new container will have 25 times the volume of the original container.

• The height of the new container will remain the same as the height of the original container.

The length of the radius of the new container will be --

a. 5 times the length of the radius of the original container

b. 25 times the length of the radius of the original container

c. 125 times the length of the radius of the original container

d. 625 times the length of the radius of the original container

____ 49. The volume of a cube is 27 cubic inches. What is the surface area of the cube?

a. 9 in² b. 54 in² c. 81 in² d. 162 in²

1 2 3 4 5 6 7 8 9 10–1–2–3–4–5–6–7–8–9–10 x

1

2

3

4

5

6

7

8

9

10

–1

–2

–3

–4

–5

–6

–7

–8

–9

–10

y

17 cm

12 cm

11 cm


50. Click on the grid to plot the point you want to select.

Plot the center of the circle

defined by the equation:

1 2 3 4 5 6 7 8 9 10–1–2–3–4–5–6–7–8–9–10 x

1

2

3

4

5

6

7

8

9

10

–1

–2

–3

–4

–5

–6

–7

–8

–9

–10

y


Answer Section

1. ANS: C

Order reversed and nots were added to statements.

PTS: 1 REF: 2014 Geometry SOL Exam LOC: Ch 2

TOP: Triangles and Logic KEY: symbols MSC: Question 1

2. ANS: B

Construct a isosceles triangle with the same legs above and below the line. Connect the extreme angles. The

point, S, lies on that line, which is a perpendicular bisector of .

PTS: 1 REF: 2014 Geometry SOL Exam TOP: Triangles and Logic

KEY: construction MSC: Question 2

3. ANS: C

Both 2 and 7 are acute angles and cannot add to 180.

PTS: 1 REF: 2014 Geometry SOL Exam TOP: Lines and Angles

KEY: parallel lines MSC: Question 3

4. ANS: A

The three arcs that have been drawn are the first three steps to bisect .



5. ANS: C

Have to eliminate any area that has instruments other than tuba and clarinet.

No one plays only the tuba and the clarinet.


TOP: Triangles and Logic KEY: Venn diagram

MSC: Question 5 NOT: Technology assisted question

6. ANS: A

1) Place the compass on point T and draw an arc across both sides of the angle. Without changing the

compass radius, place the compass on point S and draw a long arc crossing the ray. 2) Set the

compass so that its radius is intersections on the two rays in the drawn angle. Place the compass on

intersection point on the new ray and draw an arc intersecting the one drawn in the previous step.

Label the intersection point 3) Use the straightedge to draw ray that completes the angle



7. ANS: C PTS: 1 REF: 2014 Geometry SOL Exam

LOC: Ch 2 TOP: Triangles and Logic KEY: Law of Syllogism

MSC: Question 8

8. ANS: A

Original statement: If the measure of an angle is 90º, then it is a right angle.

inverse tells us to negate clauses and we get: If the measure of an angle is not 90º, then it is not a right angle.

PTS: 1 REF: 2014 Geometry SOL Exam STA: G.1 | G.1.a

LOC: Ch 2 TOP: Triangles and Logic KEY: inverse | logic

MSC: Question 13


9. ANS: B

Angles have to involve both line q and line l and have the transversal as a common line. Using combinations of

linear pairs and/or vertical angles, they need to form consecutive interior angles (since no consecutive exterior

angles theorem exists).



10. ANS: C

Corresponding angles are congruent, so x = 63



11. ANS:

50

Alternate exterior angles are congruent in parallel lines;


KEY: parallel lines MSC: Question 15 NOT: Technology assisted question

12. ANS: D

Distance formula:


KEY: distance MSC: Question 10

13. ANS:

(–9, 2)

Line g has a slope of .

Any point satisfying will be correct.

(–9, 2) is one point that solves that equation.

Go left 3 and up 2 or right 3 and down 2 from point S to get another point.


KEY: parallel lines MSC: Question 11 NOT: Technology assisted question

14. ANS: C

Slope =

2

3

1

2



KEY: slope MSC: Question 16

15. ANS: A

Perpendicular bisector cuts line segment in half



16. ANS: A

Reflection over line , then you exchange the x and y values

PTS: 1 REF: 2014 Geometry SOL Exam STA: G.3

LOC: Ch 9 TOP: Coordinate Relations and Transformations

KEY: reflections MSC: Question 14

17. ANS: A

Same lengths opposite same angle measures (even if triangles have been flipped -- put in the third angle

measures!)


KEY: congruent triangles MSC: Question 23

18. ANS: D



19. ANS: D

x = k is a vertical line and y = h is a horizontal line. Lines of symmetry cut the figure in half.

PTS: 1 REF: 2014 Geometry SOL Exam

TOP: Coordinate Relations and Transformations KEY: symmetry

MSC: Question 17

20. ANS: D

x is the adjacent side in the right triangle, so we use trigonometry:


TOP: Triangles and Logic KEY: trigonometry

MSC: Question 19

21. ANS: D

These are three of the four congruent triangles in a rhombus. SSS or SAS (with perpendicular diagonals)



TOP: Triangles and Logic KEY: triangle congruence

MSC: Question 20

22. ANS:

27 71

Largest side - smallest side < x < smallest side + largest side

49 - 22 < x < 22 + 49

27 < x < 71


TOP: Triangles and Logic KEY: triangle sides


23. ANS: D

Must satisfy the Pythagorean theorem.


TOP: Triangles and Logic KEY: Pythagorean MSC: Question 22

24. ANS: B

Missing angle is 66 and represents the middle angle; oboe players (ones not mentioned in the smallest angle)

form the smallest side and cornet players (ones not mentioned in the largest angle) form the largest side.


TOP: Triangles and Logic KEY: triangle sides

MSC: Question 24

25. ANS: C

Pythagorean Theorem, special case right

triangles or trig can solve this

Since all sides of an equilateral triangle are

congruent, then the hypotenuse of the folded

triangle is 18.

The side opposite a 60 degree angle is .

Another way to solve it is using trig:


TOP: Triangles and Logic KEY: trigonometry | special case right triangles | Pythagorean

MSC: Question 25

26. ANS: A


Isosceles triangle. Base side is smaller than original base side, so other sides (isosceles) must be smaller than

original.


KEY: similar triangles MSC: Question 26

27. ANS:

Reflexive and SSS

A side is congruent to itself because of the Reflexive property

3 Sides are congruent; so the SSS Thrm needs to be used


TOP: Triangles and Logic KEY: congruent triangles | proof

MSC: Question 27 NOT: technology assisted

28. ANS: D

Need to use trig: sin --> opposite side and hypotenuse


TOP: Triangles and Logic KEY: trigonometry

MSC: Question 28

29. ANS:

14

PTS: 1 REF: 2014 Geometry SOL Exam TOP: Polygons and Circles

KEY: quadrilaterals MSC: Question 33 NOT: Technology assisted question

30. ANS: C

The rule is that any two sides must be greater than the third in a triangle. We add the two smallest two numbers

together and if its bigger than the largest number then those numbers will form a triangle. Only 19 cm, 21 cm,

18 cm meets that rule.

PTS: 1 REF: 2014 Geometry SOL Exam STA: G.6

LOC: Ch 5 TOP: Triangles and Logic KEY: triangles

MSC: Question 31

31. ANS: C

Match 90º angles and then short to short and long to long legs



32. ANS: D

Given an angle and a included side; the vertical angles add the final angle for ASA



KEY: congruent triangles MSC: Question 30

33. ANS: D

AA Triangle similarity theorem; included angle M is the shared angle.



34. ANS: B

Interior angles for triangle is 60 and for pentagon is 108 for a total of 168.


KEY: interior angles MSC: Question 34

35. ANS: D

From SOL formula sheet equation of a circle:

center at (–6, –5): with

Remember that a negative of a negative is a positive.


TOP: Polygons and Circles KEY: circles | circle equation

MSC: Question 35

36. ANS: D

Surface area = surface area of cylinder - base covered by the cone + lateral area of cone

PTS: 1 REF: 2014 Geometry SOL Exam TOP: Three-Dimensional Figures

KEY: surface area MSC: Question 36

37. ANS: D

Rectangular prism surface area: new height is 5.5 cm (3 + 2.5).

New SA:

PTS: 1 REF: 2014 Geometry SOL Exam KEY: surface area

MSC: Question 38

38. ANS: A

Inscribed angles ATB and AKB share the same arc and therefore have the same measure.

The 3 angles inside the triangle not containing y must add to 180; so


TOP: Polygons and Circles KEY: circles | angles

MSC: Question 37

39. ANS: B


Since the diagonals of a rhombus bisect opposite angles, then angles CHG, CHW and CYG are all 35°. The

three angles inside each triangle must add to 180° and the diagonals are perpendicular, so all angle C’s are 90°.


KEY: angles | quadrilaterals MSC: Question 39

40. ANS: A

Given the center and the diameter (twice the radius) we can figure out the equation of circle L.

Now plug in the given points and see which satisfy the equation:


TOP: Polygons and Circles KEY: circle equation

MSC: Question 40

41. ANS: A

Leg angles in an isosceles trapezoid are supplementary; so the angle in the trapeziod next to x is 122°. A

regular octagon has an interior angle of 135° (Int + Ext = 180 and Ext = 360/8 = 45)

Once around a point is 360°; so °


KEY: interior angles | exterior angle MSC: Question 47

42. ANS: B

We are finding the length of the arc(railing) in a circle with a radius of 38 feet and a central angle of the arc of

66°.


TOP: Polygons and Circles KEY: circles | arc length

MSC: Question 41

43. ANS: C

Interior angles of a hexagon (6-sided figure) is found with (n-2) x 180 = 720



KEY: interior angles MSC: Question 42

44. ANS: B

Area of a sector is the area of the circle times the ratio of the central angle divided by 360.


TOP: Polygons and Circles KEY: circles | sector area

MSC: Question 45

45. ANS:

64

Volume is a cubic relationship, so the ratio of the radii (4:7) must be cubed: 64:343


TOP: Three-Dimensional Figures KEY: spheres | ratios

MSC: Question 46 NOT: Technology assisted

46. ANS: A

Diagonals in a rectangle are the same length and bisect each other. The intersection is the mipoint between the

two vertices along that diagonal. If one vertex is located at (–8, 8), then it was right 8 and down 4 to get to the

midpoint (0, 4). We have to travel the same distance to get to the other endpoint (0 + 8, 4 - 4) or (8, 0).

PTS: 1 REF: 2014 Geometry SOL Exam

TOP: Coordinate Relations and Transformations KEY: quadrilaterals | diagonals

MSC: Question 44

47. ANS: C

Volume of a pyramid: where B is area of the base and h is the height


KEY: volume MSC: Question 49

48. ANS: A

Volume of a cylinder:

If height stays the same and the volume is 25 times as large, then the radius has to quintrouple -- 5 times the

length of the radius of the original container


KEY: volume MSC: Question 50

49. ANS: B

The formula for the volume of a cube is V = s³. The formula for surface area is SA = 6s².



TOP: Three-Dimensional Figures KEY: volume | surface area

MSC: Question 43

50. ANS:

(–7, –8)

From the Geometry equation sheet:

Equation of a circle

so center is

(h, k) or (–7, –8) with radius = 4


TOP: Coordinate Relations and Transformations KEY: circle equation


(–7, –7)

1 2 3 4 5 6 7 8 9 10–1–2–3–4–5–6–7–8–9–10 x

1

2

3

4

5

6

7

8

9

10

–1

–2

–3

–4

–5

–6

–7

–8

–9

–10

y

Documents

X G U A - Quia a right circular cylinder and a right circular cone. cm Which is closest to the surface area of the contianer? a. 1175 cm² b. 1935 cm² c. 2315 cm² d. 1555 cm²