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WorksheetsGeometry EOC - Fall 2024
Total questions: 100
Worksheet time: 4hrs 58mins
How do you copy a line segment using only a compass and a straight edge? Example Line segment XW
Put the compass's point on point W
adjust the compass's width to point X
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
Pick a pont Z on the arc, and draw a line from Y to Z using the straightedge.
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?
Assume the two angles are not congruent.
Assume the two angles are supplementary to the different angle
Assume the two angles are complementary to the same angle.
Assume the two angles are congruent to the supplementary angle.
Which translation will move the blue shape to the green shape?
3 Left
3 Down
3 Right
3 Up
2 Right
3 Up
2 Left
3 Down
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?
50 degrees
60 degrees
70 degrees
80 degrees
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.
(x, y) →(-x, y)
(x, y) →( x,-y)
(x, y) → (-y, x)
(x, y) → (y,x)
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
y=3x+2
y=x-2
y=-1/3x -2
y= -1/2x -5
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?
Based on the two triangles' markings, which statement is true?
Which statement must be true?
Which statement is true?
Proof involving indirect reasoning. Also called proof by contradiction
Direct reasoning
Indirect reasoning
Direct proof
Indirect Proof
The second step of an indirect proof is to ____?
assume the negation of the given
assume the negation of what you are trying to prove
conclude the prove is true
contradict the given using logical statements based on the initial assumption
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.
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?
1.34 ft2
16.04 ft2
192.5 ft2
2,310 ft2
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?
The containers with the rectangular base are the best value because they have less volume per pack.
The containers with the rectangular base are the best value because they have greater volume per pack.
The containers with the square base are the best value because they have greater volume per pack.
The containers with the square base are the best value because they have less volume per pack.
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?
5π
15.47π
18.77π
20π
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?
Construction A
Construction B
Construction C
Construction D
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
B
C
D
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. 0.11
B. 0.20
C. 0.43
D. 0.75
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?
Lisa’s method is correct because the people who have pets and kids should not be counted at all.
Lisa’s method is correct because the people who have pets and kids should be counted exactly once.
Lisa’s method is not correct because she is not counting the people who have pets and kids at all.
Lisa’s method is not correct because she is not counting the people who have pets and kids twice.
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?
0.14
0.16
0.18
0.20
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?
1/8
2/8
5/8
7/8
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?
0
1
2
3
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)
What is the reason for step 4?
Given
Alternate Interior Angle Theoren
Alternate Exterior Angle Theorem
Transitive property of Congruence
A Dilation is performed with center of dilation at the origin. Which square could be the image?
LMNO
PQRO
STUQ
VQWX
What is the reason for statement 5?
AAS
ASA
SAS
SSS
On a coordinate plane ΔABC , 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 ?
(x,y)→(3x,3y+3)
(x,y)→(3x, 3y−3)
(x,y)→(4x+10,4y+8)
(x,y)→(4x−10, 4y−8)
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?
3
4
10
11
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?
16
23
64
90
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?
300
200
360
500
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)
36.30
45.80
117.30
134.20
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)
1180
380
1280
520
In the diagram LW is parallel to ST. RL=6cm, LS=3cm, and WT =4cm. What is the value of x?
5
7
8
12
Which of these statements must be true? Select all that apply.
∠A≅∠D and ∠B≅∠E
ΔABC∼ΔEDC
Dilation by a factor of ACEC centered at point C followed by a rotation of 180° about point C , Maps ΔABC to ΔEDC .
Rotation 180° about point C followed by a dilation by a factor of ACEC centered at pint C , maps ΔADC to ΔEDC .
Dilation by a factor of ACEC centered at point C followed by a reflection across the line through C parallel to AB , maps ΔABC to ΔEDC .
Which transformation maps ΔABC onto ΔA′B′C′ ?
Translation 4 units right and 4 units down
reflection over the x-axis
dilation by a factor of 1 about the origin
rotation 180° about the origin
Which sequence of rigid motion will prove ΔABC≅ΔRST ?
line of reflection over y=x
rotation centered at (1,0)
a line of reflection over x−axis followed by a translation of 6 units to the right.
a line of reflection over x−axis followed by a line of reflection over y=1 .
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.
1.59 m
1.62 m
1.67 m
1.76 m
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?
4 in and 6 in
6 in and 8 in
8 in and 12 in
12 in and 16 in
ΔRST is translated 5 units left and 3 units down and then reflected over the line y=x . ΔJKL is congruent to the final image of ΔRST . Select all statements that must be true.
ΔRST≅ΔJKL
There is a sequence of transformations that would map ΔJKL onto ΔRST .
∠K is congruent to an angle of ΔRST .
ΔJKL∼ΔRST with a scale factor of 8
The perimeter , in cm of ΔJKL is equal to 2 more than the perimeter, in cm, of ΔRST .
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?
25,434 ft2
101,736 ft2
196,250 ft2
785,000 ft2
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?
25 ft
245 ft
250 ft
225 ft
In the figure shown, Roland is to prove that GH ≅HJ
AAS
ASA
SAS
SSS
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.
11.2 cm
12.cm
13.2 cm
10.8 cm
A large water basin is in the shape of a right cylinder. The inside of the basin has a diameter of 8 41 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 21 foot from the top.
123 ft3
143 ft3
134 ft3
534 ft3
Fill in the missing proofs.
Vertical Angles are Congruent, SAS(Side-Angle-Side)
Reflexive Property, SAS(Side-Angle-Side)
Reflexive Property, Vertical Angles are Congruent
Transitive Property, SSS(Side-Side-Side)
Select ALL the true statements about an image after a dilation.
The image is a different shape than the preimage.
The image is a different size than the preimage.
The image has the same angle measures as the preimage.
The image is similar to the preimage.
The image has the same side lengths as the preimage.
Which segment is skew to CD ?
AE
BC
GH
DH
AB
Which postulate can be used to prove ∆ABC ≅ ∆EDC?
AAA
SSS
SAS
ASA
SSA
Which congruence statement correctly describes the relationship between the following triangles?
∆ABC ≅ ∆XYZ
∆ABC ≅ ∆XZY
∆ABC ≅ ∆ZYX
∆ABC ≅ ∆YXZ
∆ABC ≅ ∆YZX
∆ABC is similar to ∆XYZ. What is the measure of AC ?
7
8
9
10
11
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?
Hector does not need to know anything else about triangles A or B
Hector needs to know the length of any corresponding side in both triangles
Hector needs to know all three angles in triangle A are congruent to the corresponding angles in triangle B
Hector needs to know the length of the side between the corresponding angles on each triangle.
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 translation of two units to the right and two units down
A counterclockwise rotation of 180 degrees around the origin
A reflection over the x-axis
A dilation with a scale factor of 2 and centered at the origin
What is the equation of the circle shown on the graph?
(x−2)2+(y−1)2=9
(x−2)2+(y+1)2=9
(x+2)2+(y−1)2=9
(x+2)2+(y−1)2=3
(x−2)2+(y+1)2=3
What is the measure of each interior angle in a regular dodecagon?
110°
130°
150°
170°
190°
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.
m∠2 = 90°
m∠6 = 90°
m∠3 = m∠6
m∠1 + m∠6 = 90°
m∠4 + m∠5 = 90°
Which statements should be used to prove that the measure of ∠1 and ∠5 sum is 180°?
∠1 and ∠2 form a linear pair; ∠3 and ∠4 form a linear pair
∠5 and ∠7 are congruent as vertical angles; ∠6 and ∠8 are congruent as vertical angles
∠1 and ∠3 are congruent as vertical angles; ∠7 and ∠8 form a linear pair
undefinedandundefinedare congruent as corresponding angles;undefinedandundefinedform a linear pair
Which statement justifies why the constructed line passing through the given point A is parallel to CD ?
When two lines are each perpendicular to a third line, the lines are parallel
When two lines are each parallel to a third line, the lines are parallel
When two lines are intersected by a transversal and alternate interior angles are congruent, the lines are parallel
When two lines are intersected by a transversal and corresponding angles are congruent, the lines are parallel
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 equals the slope of CD and the slope of BC equals the slope of AD ."
Tammy says, “We show that AC=BD and that (slope of AC ) × (slope of BD ) = -1.”
Only Jillian’s is valid.
Only Tammy’s is valid.
Both are valid.
Neither is valid.
Circle P has tangents XY and ZY and chords WX and WZ as shown in this figure. The measure of ∠ZWX = 70°. What is the measure, in degrees, of ∠XYZ?
What is the definition of a line segment?
A line segment is a line that extends infinitely in both directions.
A line segment is a line that intersects with other lines at multiple points.
A line segment is a curved line with no endpoints.
A line segment is a part of a line that is bounded by two distinct endpoints.
What is the definition of a ray?
A ray is a part of a line that has one endpoint and extends infinitely in one direction.
A ray is a curved line segment with one endpoint.
A ray is a straight line segment with two endpoints.
A ray is a part of a line that has two endpoints.
What is the definition of an angle?
A geometric figure formed by two rays that share a common endpoint, called the vertex.
A line segment connecting two points.
A three-dimensional shape with six faces.
A straight line that extends infinitely in both directions.
What is the difference between acute and obtuse angles?
An acute angle measures more than 90 degrees.
An obtuse angle measures less than 90 degrees.
An acute angle measures exactly 90 degrees.
An acute angle measures less than 90 degrees, while an obtuse angle measures more than 90 degrees but less than 180 degrees.
What is the definition of a straight angle?
An angle that measures less than 180 degrees.
An angle that measures exactly 180 degrees.
An angle that measures more than 180 degrees.
An angle that measures exactly 90 degrees.
What is the definition of a right angle?
An angle that measures less than 90 degrees.
An angle that measures more than 90 degrees.
An angle that measures exactly 180 degrees.
An angle that measures exactly 90 degrees.
What is the definition of a perpendicular line?
A line that intersects another line at a right angle (90 degrees).
A line that does not intersect another line.
A line that intersects another line at an obtuse angle (greater than 90 degrees).
A line that intersects another line at a acute angle (less than 90 degrees).
What is the definition of a parallel line?
Lines that intersect at multiple points.
Lines that never intersect
Lines that intersect at one point.
Lines that are perpendicular to each other.
What is the sum of the angles in a triangle?
180
270
360
90
What is the definition of a congruent angle?
Angles that have the same measure or size.
Angles that have different measures.
Angles that are parallel to each other.
Angles that intersect at a point.
Write a rule for the translation.
(x -1, y + 2)
(x -2, y + 1)
(x +2, y - 1)
(x +1, y - 2)
Reflect Point C over the line x = 1
(-1, 2)
(3, 0)
(0, 2)
(3, -1)
Given the point Y at (5, 2), where would the image be after the following translation: (x + 2, y - 7)?
(7, 7)
(3, 9)
(4, -5)
(7, -5)
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
B
C
D
Choose the correct scale factor:
2.5
1.5
3.5
4
Which of the following describes the sequence of transformations shown?
Reflect across the x-axis and then rotate -90 degrees cw around the origin
Rotate 90 degrees cw around the origin and then translate down.
Reflect across the x-axis and then reflect across the y-axis.
Translate up and then rotate 90 degrees ccw about the origin.
A rectangular prism has the dimensions shown. What is the volume, in cubic inches, of the rectangular prism?
143
239
420
478
The formula for the surface area of a cone is S=πr2+πrl , where r is the radius of the cone and l 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?
240
320
490
.
860
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?
1,755
2,770
6,620
13,345
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.
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 S , the surface area of a square pyramid, uses b to represent a side length of the base and x to represent the slant height.
Which sentence best describes the slant height of the square pyramid?
The slant height measures 6 centimeters, because the formula for the surface area of a square pyramid is S=b2+2bx and b is 8 centimeters.
The slant height measures 9 centimeters, because the formula for the surface area of a square pyramid is s=b2+4bx and b is 4 centimeters.
The slant height measures 10 centimeters, because the formula for the surface area of a square pyramid is S=4bx and b is 4 centimeters.
The slant height measures 20 centimeters, because the formula for the surface area of a square pyramid is S=bx and b is 8 centimeters.
Which objects have volumes that are best modeled by the formula V = πr2 h? Select the two correct answers.
a computer
a soccer ball
a can of juice
a round balloon
a roll of paper towels
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?
Quadrilateral ABCD is a rhombus but not a square.
Quadrilateral ABCD is a rectangle but not a square.
Quadrilateral ABCD is a parallelogram but not a rectangle.
Quadrilateral ABCD is a trapezoid but not a parallelogram.
The diagram shows △ ABC and △ DEF. Which statements are true for △ ABC and △ DEF? Select the three correct answers.
△ ABC ≅ △ DEF
ABC~△ DEF
sin A = 53 , sin D = 53 , sin B = 54 , sin E = 54
tan A = ABBC tan D = EDEF
The scale factor of △ ABC to △ DEF is 1:2.
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
m∠J = 80°
m∠Q = 60°
m∠J = m∠L
m∠P = d(m∠J)
m∠P + m∠L = 160°
In the coordinate plane, a single transformation maps scalene △ ABC to △ DEF,
so that △ ABC ≅ △ FDE. Which statement must be true?
If the transformation was a 90°-clockwise rotation about the origin, then
AC ≅ FE .
If the transformation was a 90°-clockwise rotation about the origin, then ∠A ≅ ∠D.
If the transformation was a dilation with a scale factor of 2 centered at the origin, then BC ≅ DE.
If the transformation was a dilation with a scale factor of 2 centered at the origin, then ∠C ≅ ∠E
The image of EF after a sequence of transformations is 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 vertical shift of 3 units
a horizontal shift of 2 units
a reflection over the y-axis
a dilation about the origin by a scale factor of 3
