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Worksheets

Geometry EOC - Fall 2024

Total questions: 100

Worksheet time: 4hrs 58mins

Name
Class
Date
1.

How do you copy a line segment using only a compass and a straight edge? Example Line segment XW

a)

Put the compass's point on point W

b)

adjust the compass's width to point X

c)

Without adjusting the compass width, place its point on Y, and draw an arc where the other endpoint of the new line segment is to be

d)

Pick a pont Z on the arc, and draw a line from Y to Z using the straightedge.

1)
2)
3)
4)
2.

If two angles are supplementary to the same angle, the two angles are congruent. Which of the following assumptions can be used to do a proof by contradiction?

a)

Assume the two angles are not congruent.

b)

Assume the two angles are supplementary to the different angle

c)

Assume the two angles are complementary to the same angle.

d)

Assume the two angles are congruent to the supplementary angle.

3.

Which translation will move the blue shape to the green shape?

a)

3 Left

3 Down

b)

3 Right

3 Up

c)

2 Right

3 Up

d)

2 Left

3 Down

4.

Marisa is building a bookstand with a triangular base. If two angles of the triangular bas measure 75 degrees and 35 degrees, what is the measure of the third angle?

a)

50 degrees

b)

60 degrees

c)

70 degrees

d)

80 degrees

5.

A line segment has a length of 10 units. The line segment undergoes a translation up 5 units and left 5 units form its original position. The length of the resulting line segment will be ​ (a)   the length of the original line segment since translations ​ (b)   the lengths of line segments.

Choose from the below words
the same as
twice as long
preserve
do not preserve
6.
a)

(x, y) →(-x, y)

b)

(x, y) →( x,-y)

c)

(x, y) → (-y, x)

d)

(x, y) → (y,x)

7.

Organize these options into the right categories

Categorize the following

Triangle 5 is the result of translating Triangle 1 right 6 units and down 6 units

Triangle 1 is the result of translating Triangle 3 left 6 units and up 2 units

Triangle 2 is the result of dilating Triangle 3 by a scale factor of 2 ONLY

Triangle 4 is the result of rotating Triangle 5 by 90- counter clockwise about the origin

True
False
8.

a)

y=3x+2

b)

y=x-2

c)

y=-1/3x -2

d)

y= -1/2x -5

9.
a)

b)

c)

d)

10.

Triangle ABC has vertices located at the points a(1, -3), B (5, 0), and C (6,-4) on the coordinate plane. Which name best describes triangle ABC?

a)

b)

c)

d)

11.
a)

b)

c)

d)

12.

Based on the two triangles' markings, which statement is true?

a)

b)

c)

d)

13.

Which statement must be true?

a)

b)

c)

d)

14.

Which statement is true?

a)

b)

c)

d)

15.
The first step of an indirect proof is to ____?
a)
write the given
b)
assume the negation of the given
c)
assume the negation of what you are trying to prove
d)
contradict the given
16.

Proof involving indirect reasoning. Also called proof by contradiction

a)

Direct reasoning

b)

Indirect reasoning

c)

Direct proof

d)

Indirect Proof

17.

The second step of an indirect proof is to ____?

a)

assume the negation of the given

b)

assume the negation of what you are trying to prove

c)

conclude the prove is true

d)

contradict the given using logical statements based on the initial assumption

18.

The points A (-3,3), B (0,7) C(4,10), and D (1,6) creates a parallelogram ABCD what is the perimeter of the parallelogram in Units.

a)
The perimeter of the parallelogram ABCD is 18 units.
b)
The perimeter of the parallelogram ABCD is 15 units.
c)
The perimeter of the parallelogram ABCD is 20 units.
d)
The perimeter of the parallelogram ABCD is 12 units.
19.

What is the volume, in cubic feet, of the piece of wood that is 5.5 inches wide, 3.5 inches thick, and 10 feet long?

a)

1.34 ft2

b)

16.04 ft2

c)

192.5 ft2

d)

2,310 ft2

20.

A restaurant owner wants to buy containers for storing. The table shows two types of containers she is considering. Each pack costs the same amount.

Which statement best justifies the containers are the best value per pack?

a)

The containers with the rectangular base are the best value because they have less volume per pack.

b)

The containers with the rectangular base are the best value because they have greater volume per pack.

c)

The containers with the square base are the best value because they have greater volume per pack.

d)

The containers with the square base are the best value because they have less volume per pack.

21.

Samuel measured the height and radius of a cylindrical container to the nearest tenth of a meter. The measurements are given.

The height is 5.1 meters.

The radius of the base is 1.8 meters.

What could be the measure, in cubic meters, Samuel uses for the volume of the container?

a)

b)

15.47π

c)

18.77π

d)

20π

22.

Which construction would be most helpful to begin his construction if Micah wants to find a point that is equidistant from the three vertices of a triangle?

a)

Construction A

b)

Construction B

c)

Construction C

d)

Construction D

23.

At a school, 15 students play on the basketball team and 14 students play on the soccer

team. Some students play on both teams.

One student is selected at random.

• Event E is when the selected student plays on the basketball team.

• Event F is when the selected student plays on the soccer team.


Which Venn diagram has only the set E∩F shaded?

a)

A

b)

B

c)

C

d)

D

24.

A survey was conducted to predict if high school students will eat food served in the

cafeteria. The results for the 410 students surveyed are shown in the table.

Which number is closest to the probability that a student will not eat food served in the school cafeteria, given that the student is in 10th grade?

a)

A. 0.11

b)

B. 0.20

c)

C. 0.43

d)

D. 0.75

25.

A total of 100 adults responded to a survey that asked whether they had any pets and

whether they had any kids. The results of the survey are shown in the table.

Lisa wants to determine the number of people who have pets or kids. She adds 63 and

46, then subtracts 34.


Which statement explains whether Lisa’s method is correct?

a)

Lisa’s method is correct because the people who have pets and kids should not be counted at all.

b)

Lisa’s method is correct because the people who have pets and kids should be counted exactly once.

c)

Lisa’s method is not correct because she is not counting the people who have pets and kids at all.

d)

Lisa’s method is not correct because she is not counting the people who have pets and kids twice.

26.

A high school has 250 twelfth-grade students. The numbers of twelfth-grade students who

were members of the track team and the band are described.

• 25 twelfth-grade students were members of the track team.

• 20 twelfth-grade students were members of the band.

• 5 twelfth-grade students were members of both the track team and the band.


If 1 twelfth-grade student from the high school is randomly selected, what is the probability that the student will be a member of the track team or a member of the band?

a)

0.14

b)

0.16

c)

0.18

d)

0.20

27.

Circle A is shown with a radius of 8 inches. Central angle BAC measures 45°. The radius of the smaller circle inside circle A is 4 inches. A point is selected at random inside circle A.

What is the probability that the point is neither in sector BAC nor in the smaller circle?

a)

1/8

b)

2/8

c)

5/8

d)

7/8

28.

The faces of a fair number cube are labeled 1 through 6. The number cube is rolled once.

Two events are described.

• A possible outcome is the event that the number 1 is rolled.

• Another possible outcome is the event that an even number is rolled.

What is the total number of outcomes that is not in either of these events?



a)

0

b)

1

c)

2

d)

3

29.

A circle has a center at (6, 2). Point B (12, 15.75) is on the circle.


What is the radius of the circle, rounded to the nearest whole unit?


Enter your answer in the space provided.




(a)  

30.

What is the reason for step 4?

a)

Given

b)

Alternate Interior Angle Theoren

c)

Alternate Exterior Angle Theorem

d)

Transitive property of Congruence

31.

A Dilation is performed with center of dilation at the origin. Which square could be the image?

a)

LMNO

b)

PQRO

c)

STUQ

d)

VQWX

32.

What is the reason for statement 5?

a)

AAS

b)

ASA

c)

SAS

d)

SSS

33.

On a coordinate plane ΔABC\Delta ABC  ,  has vertices at A(10,5), B (10,15) and C (5,5).    has vertices at A’(30,12), B’(30,52)  and C’ (10,12).  Which transformation maps   onto  ?

a)

(x,y)(3x,3y+3)\left(x,y\right)\rightarrow\left(3x,3y+3\right)

b)

(x,y)(3x, 3y3)\left(x,y\right)\rightarrow\left(3x,\ 3y-3\right)

c)

(x,y)(4x+10,4y+8)\left(x,y\right)\rightarrow\left(4x+10,4y+8\right)

d)

(x,y)(4x10, 4y8)\left(x,y\right)\rightarrow\left(4x-10,\ 4y-8\right)

34.

A construction company is hired to resurface a straight section of road.

* The section is 100 yd long and 18 feet wide.

* The company's truck can haul 250 cubic feet of gravel per load.

What is the minimum number of truckloads required to completely cover the section of road to a depth of 6 inches?

a)

3

b)

4

c)

10

d)

11

35.

Dante rides his bicycle due west at 10 miles per hour. Annie rides her bicycle due north at 12.5 miles per hour. If they both leave Annie's house at the same time, approximately how far apart, in miles, are they after 4 hours?

a)

16

b)

23

c)

64

d)

90

36.

Michael rides his boat due east at 20 miles per hour. Brianna rides her boat due south at 30 miles per hour. if they both leave the dock at the same time , approximately how far apart, in miles are they after 10 hours?

a)

300

b)

200

c)

360

d)

500

37.

A triangular earring has side length of 1.5 cm, 2 cm, and 3 cm. What is the approximate measure in degrees of the largest angel of the triangular earring? HINT(Law of cosine)

a)

36.3036.3^0  

b)

45.8045.8^0  

c)

117.30117.3^0  

d)

134.20134.2^0  

38.

A rhombus has side lengths of 25 inches. The diagonal opposite the obtuse angles is 45 inches. What is the measure of the obtuse angle to the nearest degree? 

HINT (Law of cosine)

a)

1180118^0

b)

38038^0

c)

1280128^0

d)

52052^0

39.

In the diagram LW is parallel to ST. RL=6cm, LS=3cm, and WT =4cm. What is the value of x?

a)

5

b)

7

c)

8

d)

12

40.

Which of these statements must be true? Select all that apply.

a)

AD \angle A\cong\angle D\ and BE\angle B\cong\angle E

b)

ΔABCΔEDC\Delta ABC\sim\Delta EDC

c)

Dilation by a factor of ECAC\frac{EC}{AC} centered at point CC followed by a rotation of 180°180^{\degree} about point CC , Maps ΔABC to ΔEDC\Delta ABC\ to\ \Delta EDC .

d)

Rotation 180°180^{\degree} about point CC followed by a dilation by a factor of ECAC\frac{EC}{AC} centered at pint CC , maps ΔADC to ΔEDC\Delta ADC\ to\ \Delta EDC .

e)

Dilation by a factor of ECAC\frac{EC}{AC} centered at point CC followed by a reflection across the line through CC parallel to AB\overline{AB} , maps ΔABC to ΔEDC\Delta ABC\ to\ \Delta EDC .

41.

 

Which transformation maps  ΔABC \Delta ABC\  onto  ΔABC\Delta A'B'C'  ?

a)

Translation 4 units right and 4 units down

b)

reflection over the x-axis

c)

dilation by a factor of 1 about the origin

d)

rotation  180°180^{\degree}  about the origin

42.

Which sequence of rigid motion will prove  ΔABCΔRST\Delta ABC\cong\Delta RST  ?

a)

line of reflection over  y=xy=x  

b)

rotation centered at  (1,0)\left(1,0\right)  

c)

a line of reflection over  xaxisx-axis  followed by a translation of 6 units to the right.

d)

a line of reflection over  xaxisx-axis  followed by a line of reflection over  y=1y=1  .

43.

The volumes of the two solids are equal, and the cross sections shown are taken at the same height above the bases. Find the missing length of the cross section of the rectangular pyramid. Round your answer to the nearest hundredth.

a)

1.59 m

b)

1.62 m

c)

1.67 m

d)

1.76 m

44.

If the volumes of the two solids are equal, find a pair of measurements that are possible lengths of the legs of the right triangular cross section?

a)

4 in and 6 in

b)

6 in and 8 in

c)

8 in and 12 in

d)

12 in and 16 in

45.

ΔRST \Delta RST\  is translated 5 units left and 3 units down and then reflected over the line  y=xy=x  .   ΔJKL\Delta JKL  is congruent to the final image of  ΔRST\Delta RST  .  Select all statements that must be true.

a)

ΔRSTΔJKL\Delta RST\cong\Delta JKL  

b)

There is a sequence of transformations that would map  ΔJKL\Delta JKL  onto  ΔRST\Delta RST  .

c)

K\angle K  is congruent to an angle of  ΔRST\Delta RST  .

d)

ΔJKLΔRST \Delta JKL\sim\Delta RST\  with a scale factor of 8

e)

The perimeter , in cm of  ΔJKL\Delta JKL  is equal to 2 more than the perimeter, in cm, of  ΔRST\Delta RST  .

46.

Lucy wants to approximate the area of a pond that is roughly circular. She knows the distances given.

Which is the closest approximation of the SURFACE AREA of the pond?

a)

25,434 ft2ft^2

b)

101,736 ft2ft^2

c)

196,250 ft2ft^2

d)

785,000 ft2785,000\ ft^2

47.

Mr. Smith wants to find the length, l, of a pond. He knows the distance shown in the diagram. What is the length in feet, of the pond?

a)

25 ft

b)

245 ft

c)

250 ft

d)

225 ft

48.

In the figure shown, Roland is to prove that  GH  HJ\overline{GH\ }\ \cong\overline{HJ}  

a)

AAS

b)

ASA

c)

SAS

d)

SSS

49.

A manufacturer is designing a new container for their chocolate-coverd almonds. Their original container was a cylinder with a height of 18 cm and diameter of 14 cm. The new container can be modeled by a rectangular prism with a square base and will contain the same amount of chocolate-covered almonds. If the new rectangular prim's height is 16 cm, determine, to the nearest tenth of a centimetre, the side length of the new container if both containers contain the same amount of almonds.

a)

11.2 cm

b)

12.cm

c)

13.2 cm

d)

10.8 cm

50.

A large water basin is in the shape of a right cylinder. The inside of the basin has a diameter of  8 148\ \frac{1}{4}  feet and height of 3 feet.  Determine to the nearest cubic foot, the number of cubic feet of water that it will take to fill the basin to a level of  12\frac{1}{2}  foot from the top.

a)

123  ft3ft^3  

b)

143  ft3ft^3  

c)

134  ft3ft^3  

d)

534  ft3ft^3  

51.
The triangles are similar, solve for the question mark.
a)
8
b)
12.5
c)
18
d)
24
52.

Fill in the missing proofs.

a)

Vertical Angles are Congruent, SAS(Side-Angle-Side)

b)

Reflexive Property, SAS(Side-Angle-Side)

c)

Reflexive Property, Vertical Angles are Congruent

d)

Transitive Property, SSS(Side-Side-Side)

53.
Which of the following describes the sequence of transformations shown?
a)
Reflect across the x-axis and then rotate -90 degrees around the origin
b)
Rotate -90 degrees around the origin and then translate down.
c)
Reflect across the x-axis and then reflect across the y-axis.
d)
Translate up and then rotate 90 degrees about the origin.
54.

Select ALL the true statements about an image after a dilation.

a)

The image is a different shape than the preimage.

b)

The image is a different size than the preimage.

c)

The image has the same angle measures as the preimage.

d)

The image is similar to the preimage.

e)

The image has the same side lengths as the preimage.

55.

Which segment is skew to CD\overline{CD} ?

a)

  AE\overline{AE}

b)

BC\overline{BC}  

c)

GH\overline{GH}  

d)

DH\overline{DH}  

e)

AB\overline{AB}  

56.

Which postulate can be used to prove ∆ABC ≅ ∆EDC?

a)

 AAA

b)

SSS

c)

SAS

d)

ASA

e)

SSA

57.

Which congruence statement correctly describes the relationship between the following triangles?

a)

∆ABC ≅ ∆XYZ

b)

∆ABC ≅ ∆XZY

c)

∆ABC ≅ ∆ZYX

d)

∆ABC ≅ ∆YXZ

e)

∆ABC ≅ ∆YZX

58.

∆ABC is similar to ∆XYZ. What is the measure of AC\overline{AC} ?

a)

 7

b)

c)

9

d)

10

e)

 11

59.

Hector knows two angles in triangle A are congruent to two angles in triangle B, what else does Hector need to know to prove that triangles A and B are similar?

a)

Hector does not need to know anything else about triangles A or B

b)

Hector needs to know the length of any corresponding side in both triangles

c)

Hector needs to know all three angles in triangle A are congruent to the corresponding angles in triangle B

d)

Hector needs to know the length of the side between the corresponding angles on each triangle.

60.

The vertices of ΔJKL have coordinates J(5, 1), K (-2 -3), and L(-4, 1). Under which transformation is the image ΔJ′K′L′ NOT congruent to ΔJKL?

a)

A translation of two units to the right and two units down

b)

A counterclockwise rotation of 180 degrees around the origin

c)

A reflection over the x-axis

d)

A dilation with a scale factor of 2 and centered at the origin

61.

What is the equation of the circle shown on the graph?

a)

(x2)2+(y1)2=9\left(x-2\right)^2+\left(y-1\right)^2=9  

b)

(x2)2+(y+1)2=9\left(x-2\right)^2+\left(y+1\right)^2=9  

c)

(x+2)2+(y1)2=9\left(x+2\right)^2+\left(y-1\right)^2=9

d)

(x+2)2+(y1)2=3\left(x+2\right)^2+\left(y-1\right)^2=3  

e)

(x2)2+(y+1)2=3\left(x-2\right)^2+\left(y+1\right)^2=3  

62.

What is the measure of each interior angle in a regular dodecagon?

a)

110°

b)

130°

c)

150°

d)

170°

e)

190°

63.

The figure shows lines r, n, and p intersecting to form angles numbered 1, 2, 3, 4, 5, and 6. All three lines lie in the same plane.

Based on the figure, which of the individual statements would provide enough information to conclude that line r is perpendicular to line p? Select ALL that apply.

a)

m∠2 = 90°

b)

m∠6 = 90°

c)

m∠3 = m∠6

d)

m∠1 + m∠6 = 90°

e)

m∠4 + m∠5 = 90°

64.

Which statements should be used to prove that the measure of 1\angle1 and 5\angle5 sum is 180°?

a)

1\angle1 and 2\angle2 form a linear pair; 3\angle3 and 4\angle4 form a linear pair

b)

  5\angle5 and 7\angle7 are congruent as vertical angles;  6\angle6 and 8\angle8 are congruent as vertical angles

c)

1\angle1 and 3\angle3  are congruent as vertical angles; 7\angle7 and  8\angle8  form a linear pair

d)

undefinedandundefinedare congruent as corresponding angles;undefinedandundefinedform a linear pair

65.

Which statement justifies why the constructed line passing through the given point A is parallel to CD\overline{CD}

a)

 When two lines are each perpendicular to a third line, the lines  are parallel

b)

When two lines are each parallel to a third line, the lines are  parallel

c)

When two lines are intersected by a transversal and alternate  interior angles are congruent, the lines are parallel

d)

When two lines are intersected by a transversal and  corresponding angles are congruent, the lines are parallel

66.

Jillian and Tammy are considering a quadrilateral ABCD. Their task is to prove it is a square. 
Jillian says, “We just need to show that the slope of AB\overline{AB} equals the slope of  CD\overline{CD} and the slope of BC\overline{BC} equals the slope of AD\overline{AD} ."    

Tammy says, “We show that AC=BDAC=BD and that (slope of  AC\overline{AC}   ) × (slope of BD\overline{BD}  ) = -1.”

Whose method of proof is valid?

a)

Only Jillian’s is valid.

b)

Only Tammy’s is valid.

c)

Both are valid.

d)

Neither is valid.

67.

Circle P has tangents XY\overline{XY} and ZY\overline{ZY} and chords WX\overline{WX} and WZ\overline{WZ} as shown in this figure. The measure of ∠ZWX = 70°. What is the measure, in degrees, of ∠XYZ?

4 lines
68.

What is the definition of a line segment?

a)

A line segment is a line that extends infinitely in both directions.

b)

A line segment is a line that intersects with other lines at multiple points.

c)

A line segment is a curved line with no endpoints.

d)

A line segment is a part of a line that is bounded by two distinct endpoints.

69.

What is the definition of a ray?

a)

A ray is a part of a line that has one endpoint and extends infinitely in one direction.

b)

A ray is a curved line segment with one endpoint.

c)

A ray is a straight line segment with two endpoints.

d)

A ray is a part of a line that has two endpoints.

70.

What is the definition of an angle?

a)

A geometric figure formed by two rays that share a common endpoint, called the vertex.

b)

A line segment connecting two points.

c)

A three-dimensional shape with six faces.

d)

A straight line that extends infinitely in both directions.

71.

What is the difference between acute and obtuse angles?

a)

An acute angle measures more than 90 degrees.

b)

An obtuse angle measures less than 90 degrees.

c)

An acute angle measures exactly 90 degrees.

d)

An acute angle measures less than 90 degrees, while an obtuse angle measures more than 90 degrees but less than 180 degrees.

72.

What is the definition of a straight angle?

a)

An angle that measures less than 180 degrees.

b)

An angle that measures exactly 180 degrees.

c)

An angle that measures more than 180 degrees.

d)

An angle that measures exactly 90 degrees.

73.

What is the definition of a right angle?

a)

An angle that measures less than 90 degrees.

b)

An angle that measures more than 90 degrees.

c)

An angle that measures exactly 180 degrees.

d)

An angle that measures exactly 90 degrees.

74.

What is the definition of a perpendicular line?

a)

A line that intersects another line at a right angle (90 degrees).

b)

A line that does not intersect another line.

c)

A line that intersects another line at an obtuse angle (greater than 90 degrees).

d)

A line that intersects another line at a acute angle (less than 90 degrees).

75.

What is the definition of a parallel line?

a)

Lines that intersect at multiple points.

b)

Lines that never intersect

c)

Lines that intersect at one point.

d)

Lines that are perpendicular to each other.

76.

What is the sum of the angles in a triangle?

a)

180

b)

270

c)

360

d)

90

77.

What is the definition of a congruent angle?

a)

Angles that have the same measure or size.

b)

Angles that have different measures.

c)

Angles that are parallel to each other.

d)

Angles that intersect at a point.

78.

Write a rule for the translation.

a)

(x -1, y + 2)

b)

(x -2, y + 1)

c)

(x +2, y - 1)

d)

(x +1, y - 2)

79.

Reflect Point C over the line x = 1

a)

(-1, 2)

b)

(3, 0)

c)

(0, 2)

d)

(3, -1)

80.
Point (-3,-3) is rotated 360 degrees clockwise about the origin.  Where is the new point located?
a)
(3,3)
b)
(-3,3)
c)
(3,-3)
d)
(-3,-3)
81.
Identify the transformation from A to D.
a)
90o Clockwise Rotation
b)
180o Rotation
c)
270o Clockwise Rotation
d)
360o Rotation
82.

Given the point Y at (5, 2), where would the image be after the following translation: (x + 2, y - 7)?

a)

(7, 7)

b)

(3, 9)

c)

(4, -5)

d)

(7, -5)

83.
Name the series of transformations that maps ABC onto DEF
a)
reflect over x then translate left 6 up 1
b)
reflect over y then translate down 6 left 1
c)
translate right 6 down 1, then reflect over x
d)
rotate 90 clockwise then reflect over y
84.

Triangle A is rotated 270° clockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?

a)

A

b)

B

c)

C

d)

D

85.

Choose the correct scale factor:

a)

2.5

b)

1.5

c)

3.5

d)

4

86.
Dilate Point B by a scale factor of 1/2
a)
(1.5,-4)
b)
(-1.5,1)
c)
(-1,-1.5)
d)
(-2,-2)
87.
A scale factor of less than one means
a)
that the image will be larger than the pre-image.
b)
That the image will be the same as the pre-image.
c)
That you need to subtract that amount off  of each side.
d)
That the image will be a reduction of the pre-image.
88.
The point (8, 12) was dilated to become point (2, 3). What was the scale factor?
a)
½
b)
¼
c)
4
d)
2
89.

Which of the following describes the sequence of transformations shown?

a)

Reflect across the x-axis and then rotate -90 degrees cw around the origin

b)

Rotate 90 degrees cw around the origin and then translate down.

c)

Reflect across the x-axis and then reflect across the y-axis.

d)

Translate up and then rotate 90 degrees ccw about the origin.

90.

A rectangular prism has the dimensions shown. What is the volume, in cubic inches, of the rectangular prism?

a)

  • 143

b)

  • 239

c)

  • 420

d)

  • 478

91.

The formula for the surface area of a cone is S=πr2+πrlS=\pi r^2+\pi rl , where rr is the radius of the cone and ll  is the slant height. A cone has a diameter of 12 centimeters and a slant height of 10.9 centimeters. What is the surface area of the cone, to the nearest 10 square centimeters?

a)
  • 240

b)
  • 320

c)
  • 490

d)

.

  • 860

92.

An artist covers a cylindrical container with decorative paper. The container has a radius of 18 centimeters and a height of 6.5 centimeters. Which amount is closest to the number of square centimeters of decorative paper that the artist uses to cover the container?

a)

1,755

b)

2,770

c)

6,620

d)

13,345

93.

A baker makes a cake in the shape of a hemisphere with a radius of 3 inches. The baker will put the cake into a container in the shape of a rectangular prism with these dimensions.

  • a length of 7 inches

  • a width of 7 inches

  • a height of 5 inches

Complete the sentences to describe both the volume of the cake and the difference between the volume of the container and the volume of the cake.

Move the correct answer to each box. Not all answers will be used.

The volume of the cake is about​ ​ (a)  

cubic inches.

The difference between the volume of the container and the volume of the cake is about​ (b)  

cubic inches.

Choose from the below words
57
188
113
132
207
302
452
94.

A square pyramid has these measurements.

  • a surface area of 160 square centimeters

  • a base with a perimeter of 32 centimeters

A formula to determine SS , the surface area of a square pyramid, uses bb  to represent a side length of the base and xx to represent the slant height.

Which sentence best describes the slant height of the square pyramid?

a)

The slant height measures 6 centimeters, because the formula for the surface area of a square pyramid is S=b2+2bxS=b^2+2bx and b is 8 centimeters.

b)
  • The slant height measures 9 centimeters, because the formula for the surface area of a square pyramid is s=b2+4bxs=b^2+4bx and b is 4 centimeters.

c)
  • The slant height measures 10 centimeters, because the formula for the surface area of a square pyramid is S=4bx S=4bx\ and b is 4 centimeters.

d)

The slant height measures 20 centimeters, because the formula for the surface area of a square pyramid is S=bxS=bx  and b is 8 centimeters.

95.

Which objects have volumes that are best modeled by the formula V = πr2 h? Select the two correct answers.

a)

a computer

b)

a soccer ball

c)

a can of juice

d)

a round balloon

e)

a roll of paper towels

96.

The coordinates of the vertices of quadrilateral ABCD are given.

A(−2, −2) B(−7, 3) C(−3, 7) D(3, 3)

Which statement is true about quadrilateral ABCD?

a)

Quadrilateral ABCD is a rhombus but not a square.

b)

Quadrilateral ABCD is a rectangle but not a square.

c)

Quadrilateral ABCD is a parallelogram but not a rectangle.

d)

Quadrilateral ABCD is a trapezoid but not a parallelogram.

97.

The diagram shows △ ABC and △ DEF. Which statements are true for △ ABC and △ DEF? Select the three correct answers.

a)

△ ABC ≅ △ DEF

b)

ABC~△ DEF

c)

sin A = 35\frac{3}{5} , sin D = 35\frac{3}{5} , sin B = 45\frac{4}{5} , sin E = 45\frac{4}{5}

d)

tan A = BCAB\frac{BC}{AB} tan D = EFED\frac{EF}{ED}

e)

The scale factor of △ ABC to △ DEF is 1:2.

98.

In the diagram, isosceles △ PQR is the image of △ JKL after a dilation of d units, and m∠K = 20°.

Which equations must be correct? Select the three correct answers

a)

m∠J = 80°

b)

m∠Q = 60°

c)

m∠J = m∠L

d)

m∠P = d(m∠J)

e)

m∠P + m∠L = 160°

99.

In the coordinate plane, a single transformation maps scalene △ ABC to △ DEF,

so that △ ABC ≅ △ FDE. Which statement must be true?

a)

If the transformation was a 90°-clockwise rotation about the origin, then

AC\overline{AC}FE\overline{FE} .

b)

If the transformation was a 90°-clockwise rotation about the origin, then ∠A ≅ ∠D.

c)

If the transformation was a dilation with a scale factor of 2 centered at the origin, then BC ≅ DE.

d)

If the transformation was a dilation with a scale factor of 2 centered at the origin, then ∠C ≅ ∠E

100.

The image of EF\overline{EF} after a sequence of transformations is EF\overline{E'F'} . The mapping shown represents the sequence of transformations. (x, y) → (2x + 3, −2y + 3)

Which transformation is part of the sequence of transformations used to create ‾E′F′?

a)

a vertical shift of 3 units

b)

a horizontal shift of 2 units

c)

a reflection over the y-axis

d)

a dilation about the origin by a scale factor of 3