2014 Geometry Practice SOL version 2 P Q - Quia · Triangles PNU, PGU, ... 2014 Geometry Practice...

2014 Geometry Practice SOL version 2

Name: __________________________

1. Given: Parallelogram SBHE where

and .

What value of x proves this

parallelogram is a rhombus?

____ 2. The figure represents a ramp

with handrails.

Segments PQ and ST are

parallel to VW.

Segments QR and TU are

parallel to WX.

Segments PV and QW are

parallel to RX.

If , what is

?

a. 69º b. 90º c. 111º d. 159º

____ 3. 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.

____ 4. Which of the following sets of lengths can represent the measures of the sides of a right triangle?

a. 12, 16, 20 b. 8, 10, 17 c. 4, 5, 6 d. 5, 10, 13

S

B

E

H

2x + 14

3x + 8

111

P Q

R

ST

U

V W

X

R K A

T

M

1 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


____ 5. An angle congruent to

angle C is being

constructed.

Which ray could be

drawn to construct an

angle congruent to ?

a.

b.

c.

d.

6. Line l and z are cut by a transversal

What value of x proves that l // z ?

____ 7. A polygon is shown:

What is the measure

of ?

a. 57° b. 246° c. 123° d. 90°

____ 8. A rectangular pyramid is shown.

What is the volume of the pyramid?

a. 336 m³ b. 144 m³ c. 504 m³ d. 1008 m³

C

M

A

P

H

Q

l

z

137

(5x - 123)

147

P U

YT

CF

18 m

8 m

7 m


____ 9. 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 viola and the harp.

a. 6 b. 12 c. 6, 9, 10, 12 d. none

____ 10. An architect used this diagram to

design a curved balcony. He drew a

circle with a radius of 30 feet and a

central angle of 63° 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. 188 ft b. 16 ft c. 495 ft d. 33 ft

____ 11. Given: H lies on and G lies on

Which condition proves ?

a. c. b. d.

____ 12. Given : B(–9, –5) and K(5, 7) What is the slope of ?

a.

b.

c.

d.

cornet oboe

viola harp

63

30

Y

H

RG

S

7

6

7

6

6

7

6

7


____ 13. Look at this triangle.

Which triangle is similar to the given triangle?

a.

c.

b.

d.

____ 14. The floor plan for a modern home

is modeled by the composite of

the regular octogon and triangle

shown.

What is closest to the measure of

?

a. 170º b. 165º c. 155º d. 175º

J

F

D

15

cm

20.63 cm

20.63 cm

11.25 cm

21.87 cm

21.87 cm

8.44 cm 10.61 cm

14.15 cm

11.25 cm

15.47 cm15.47 cm15 cm

15 cm

20.63 cm

R

B

L


____ 15. Given: Circle U with center at (3, –8)

What equation could represent circle U?

a. c.

b. d.

____ 16. 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. Opposite sides of a rectangle are congruent.

b. Every parallelogram is a rectangle.

c. Opposite sides of a quadrilateral are congruent.

d. Every quadrilateral is a rectangle.

____ 17. Given X (–4, 8) and B (7, –3)

What is the length of ?

a. b. c. d.

____ 18. This figure is composed of

an isosceles trapezoid and a

regular octagon.

What is the value of x ?

a. 123 b. 174 c. 96 d. 102

X

B

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

51 51


____ 19. The volume of a cube is 27 cubic centimeters. What is the surface area of the cube?

a. 162 cm² b. 54 cm² c. 81 cm² d. 9 cm²

____ 20. Which diagram shows a pair of angle measures that prove lines w and n are parallel?

a.

c.

b.

d.

21. The ratio of the lengths of the radii of two sphere is 5:9. What is the ratio of the volumes of these two spheres?

____ 22. 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. 1832 in² b. 1451 in² c. 1071 in² d. 2212 in²

w n

k

h

124°

56°

w n

k

h

124° 56°

w n

k

h

124°

124°

w n

k

h

124°

124°

1 5 9 25 45 81 125 729

15 in

in8

in22


____ 23. 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 vertical angles, then the angles are congruent.

a. b. c. d.

____ 24. Quadrilateral JXGZ is shown.

If JXGZ is reflected across the

x-axis , what are the

coordinates of J’ ?

a. b. c. d.

____ 25. This figure show parallel

stair railings through points

G, V, U, and X.

What is the value of x ?

a. 25 b. 115 c. 65 d. 45

J

X

G

Z

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

G V U X

65


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

Given: Figure KAQE with diagonal

;

Complete the proof of by selecting the

reasons for the last two statements.

Statements Reasons

Given

____ 27. Which could be the lengths of three sides of a triangle?

a. 14 ft, 3 ft, 11 ft c. 28 ft, 7 ft, 20 ft

b. 21 ft, 15 ft, 12 ft d. 18 ft, 9 ft, 6 ft

____ 28. Part of a marching band formed by a triangle made with clarinet players on one side, cornet players on one side,

and oboe players on the third side.

• The angle formed by the clarinet and oboe players measured 43º

• The angle formed by the oboe and cornet players measured 72º

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

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

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

____ 29. An equilateral triangle is folded in half.

What is x, the height of the equilateral

triangle?

a. cm b. 30 cm c. cm d. 15 cm

K

E

A

Q

cm30


____ 30. Circle V has a center at (3, –5) and a diameter of 10 units. Which point lies on circle V?

a. (3, –5) b. (13, 5) c. (11, 1) d. (–1, –8)

____ 31. 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. 34.2 ft b. 26.1 ft c. 14.1 ft d. 15.3 ft

____ 32. What type of construction

is illustrated in the figure?

a. An angle congruent to c. The bisection of

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

____ 33. Parallelogram ZNXE is a

rhombus with

What is the ?

a. 34° b. 146° c. 112° d. 56°

22 ft

40

K B

QV

Z N

XE

D

34


____ 34. Triangles PNU, PGU, and ZNU

are show on the coordinate grid,

and all the vertices have

coordinates that are integers.

Which statement is true?

a. Only and are congruent.

b. Triangle PNU, , and are all congruent

c. No two triangles are congruent.

d. Only and are congruent.

____ 35. Using the information given,

which congruence postulate or

theorem can be used to prove

that ?

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

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

____ 36. In this figure, parallel lines s and t

are intersected by line j.

Which pair of angles is NOT

supplementary?

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

P

N Z

G

U

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

A

L

Y

M

E

s

t

j


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

Plot the center of the circle

defined by the equation:

____ 38. The diagonals of rectangle UBJR intersect

at the point (0, 3). One of the vertices

of the rectangle UBJR is located at (–4,

5).

Which of the following could be the

location of another vertex of this

rectangle?

a. (0, 1) b. (–2, 4) c. (0, 5) d. (4, 1)

39. The lengths of two sides of a triangle are 13 feet and 47 feet. What is the range of possible lengths, in feet, for

the third side, x, of this triangle?

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

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


____ 40. Given: Circle A

Which is the closest to the area

of the shaded sector of circle A

?

a. 249 in² b. 131 in² c. 24 in² d. 380 in²

____ 41. Given: Circle M

What is the value of y?

a. 50 b. 86 c. 94 d. 36

____ 42. Given the measures shown in the diagram, which two triangles are congruent?

a. T and W b. X and E c. T and E d. X and W

A

124

11 in

MF

W

V

G

50

94

T X

11

44

1163

63 44W E

1111

44 44

73

63


____ 43. Dani is drawing the

perpendicular bisector of .

Which point is on the

perpendicular bisector of ?

a. G b. E c. Z d. F

____ 44. 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

____ 45. Bofur attached a wire

between two poles on a hill

as shown.

Which is closest to x, the

distance between the two

poles?

a. 43 yd b. 41 yd c. 134 yd d. 123 yd

Y L

F

Z

G

E

Z F

140

17

yd


____ 46. For which polygon are both and lines of symmetry?

a.

c.

b.

d.

____ 47. A cell phone box in the shape of a rectangular

prism is shown. The height of the box is 2 cm.

The height of the original box will be increased

by 3.5 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. 464 in² b. 800 in² c. 586 in² d. 677.5 in²

____ 48. What is the contrapositive 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 the measure of an angle is not 90º, then it is a right angle.

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

2 in

16 in

14.5in


49. Line h contains the points

(–6, 5) and (8, –2).

Plot a point other than point Z

with integral coordinates that

is on a line parallel to h and

passes through point Z.

____ 50. A company is creating a new cylindrical container to replace its original cylindrical container.

• The new container will have 9 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. 3 times the length of the radius of the original container

b. 81 times the length of the radius of the original container

c. 9 times the length of the radius of the original container

d. 27 times the length of the radius of the original container

(2, –8)

Z

h

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:

6

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

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

2. ANS: D

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

KEY: parallel lines MSC: Question 18

3. ANS: B

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

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

KEY: similar triangles MSC: Question 29

4. ANS: A

Must satisfy the Pythagorean theorem.

PTS: 1 REF: 2014 Geometry SOL Exam LOC: Ch 8

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

5. ANS: D

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

compass radius, place the compass on point M 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


KEY: construction MSC: Question 6

6. ANS:

52


Alternate exterior angles are congruent in parallel lines;


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

7. ANS: C

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


KEY: interior angles MSC: Question 42

8. ANS: A

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

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

KEY: volume MSC: Question 49

9. ANS: B

Have to eliminate any area that has instruments other than viola and harp.

Only Group 12 plays the viola and the harp.


TOP: Triangles and Logic KEY: Venn diagram

MSC: Question 5 NOT: Technology assisted question

10. ANS: D

We are finding the length of the arc(railing) in a circle with a radius of 30 feet and a central angle of the arc of

63°.


TOP: Polygons and Circles KEY: circles | arc length

MSC: Question 41

11. ANS: A

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




12. ANS: D

Slope =


KEY: slope MSC: Question 16

13. ANS: B

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

original.



14. ANS: B

Once around a point is 360. Interior angles for triangle is 60 and for octogon is 135 for a total of 195.

Remaining angle is 360 - 195 = 165


KEY: interior angles MSC: Question 34

15. ANS: B

From SOL formula sheet equation of a circle:

center at (3, –8): with

Remember that a negative of a negative is a positive.


TOP: Polygons and Circles KEY: circles | circle equation

MSC: Question 35

16. ANS: A PTS: 1 REF: 2014 Geometry SOL Exam

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

MSC: Question 8

17. ANS: C

Distance formula:


KEY: distance MSC: Question 10

18. ANS: C

Leg angles in an isosceles trapezoid are supplementary; so the angle in the trapeziod next to x is 129°. 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

19. ANS: B

6

7


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

20. ANS: C

Angles have to involve both line w and line n 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).



21. ANS:

125

Volume is a cubic relationship, so the ratio of the radii (5:9) must be cubed: 125:729


TOP: Three-Dimensional Figures KEY: spheres | ratios

MSC: Question 46 NOT: Technology assisted

22. ANS: B

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


KEY: surface area MSC: Question 36

23. ANS: B

Order the same and no nots in the statements.


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

24. ANS: B

Reflection over x-axis , then you negate the 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

25. ANS: C

Corresponding angles are congruent, so x = 65



26. 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

27. ANS: B

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 12 ft, 15 ft, 21

ft 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

28. ANS: A

Missing angle is 65 and represents the middle angle; cornet players (ones not mentioned in the smallest angle)

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


TOP: Triangles and Logic KEY: triangle sides

MSC: Question 24

29. 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 30.

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

30. ANS: D

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

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



TOP: Polygons and Circles KEY: circle equation

MSC: Question 40

31. ANS: A

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


TOP: Triangles and Logic KEY: trigonometry

MSC: Question 28

32. ANS: C

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



33. ANS: D

Since the diagonals of a rhombus bisect opposite angles, then angles DEZ, DEX and DNZ are all 34°. The three

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


KEY: angles | quadrilaterals MSC: Question 39

34. ANS: B

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

35. ANS: D

Given an angle and a non-included side; the vertical angles add the final angle for AAS


KEY: congruent triangles MSC: Question 30

36. ANS: C

Both 4 and 8 are obtuse angles and cannot add to 180.




37. ANS:

(–1, –4)

From the Geometry equation sheet:

Equation of a circle

so center is

(h, k) or (–1, –4) with radius = 2


TOP: Coordinate Relations and Transformations KEY: circle equation


38. ANS: D

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 (–4, 5), then it was right 4 and down 2 to get to the

midpoint (0, 3). We have to travel the same distance to get to the other endpoint (0 + 4, 3 - 2) or (4, 1).

PTS: 1 REF: 2014 Geometry SOL Exam

TOP: Coordinate Relations and Transformations KEY: quadrilaterals | diagonals

MSC: Question 44

39. ANS:

34 60

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

47 - 13 < x < 13 + 47

34 < x < 60


TOP: Triangles and Logic KEY: triangle sides


40. 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

(–1, –1)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


MSC: Question 45

41. ANS: D

Inscribed angles WGF and WVF 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

42. ANS: B

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

measures!)


KEY: congruent triangles MSC: Question 23

43. ANS: C

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

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



44. ANS: A

Perpendicular bisector cuts line segment in half



45. ANS: C

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


TOP: Triangles and Logic KEY: trigonometry

MSC: Question 19

46. ANS: C

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

47. ANS: B

Rectangular prism surface area: new height is 5.5 cm (2 + 3.5).


New SA:

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

MSC: Question 38

48. ANS: B

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

contrapositive tells us to flip and negate clauses and we get: If it is not a right angle, then the measure of an

angle is not 90º.

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

49. ANS:

(–8, –3)

Line h has a slope of .

Any point satisfying will be correct.

(–8, –3) is one point that solves that equation.

Go left 2 and up 1 or right 2 and down 1 from point Z to get another point.


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

50. ANS: A

Volume of a cylinder:

If height stays the same and the volume is 9 times as large, then the radius has to triple -- 3 times the length of

the radius of the original container


KEY: volume MSC: Question 50

1

2

2014 Geometry Practice SOL version 2 P Q - Quia · Triangles PNU, PGU, ... 2014 Geometry Practice...

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