Free Printable Review EOC Geometry Grade 10 Mathematics

Worksheets

Review EOC Geometry Grade 10 Mathematics

Total questions: 180

Worksheet time: 2hrs 31mins

Name

Class

Date

If trapezoid , shown below, was rotated 180° clockwise about the origin, determine which notation would represent the new coordinates of J'K'L'M' ?

. If ST is reflected across the line y = x, what is the new coordinate point of T'?

Which of the following figures has been rotated 90° clockwise about the origin?

Which of the following rules describes the translation of JKLM to its image J'K'L'M' ?

Which set of figures is congruent?

Which of the following is true about the relationship between the two triangles shown below?

ASA triangle congruence can be used to prove which of the following pairs of triangles congruent?

10.

In the figure below, lines a and b are parallel. Find the value of x

11.

BD is a perpendicular bisector of AC . If AB = 4x– 6, CB = 2x + 2, and DB = 6, what is the length of AC?

12.

Analize the figure below. What is the measure of <C?

13.

In the figure shown below, ABCD is a parallelogram.

14.

If rectangle is dilated by a scale factor of 1/2 to create its image , how does the slope of AC compare to the slope of A'C'?

15.

This question has two parts:

Circle A is centered at (2,3) and contain point Z(-4,-5).

Part A: Select the method could be used to find the radius of the circle:

Find the distance between the point A and Z.

Find the equation of the line that pass through the points A and Z.

Find the sum of the vertical and horizontal distances of the translations that map the point A to point Z.

Find the sum of the vertical and horizontal distances of the translations that map the point Z to point A.

16.

This question has two parts:

Circle A is centered at (2,3) and point Z(-4,-5).

Part B: What is the length of the radius in units of the circle W.

a. $\sqrt[]{8}$

$2\sqrt[]{7}$

17.

What is the last statement and reason in this proof?

$Statement\ \Delta AKE\cong\Delta CKD\ Reason\ ASA$

$Statement\ \Delta CDE\cong\Delta CAE\ Reason\ SSS$

$Statement\ \Delta AKC\cong\Delta DKE\ Reason\ SAS$

$Statement\ \Delta ADE\cong DCA\ Reason\ SSS$

18.

Which of the following statement and reason can be used in the step number 5

$\Delta KNM\cong LMK\ \ \ \ \ \ \ ASA$

$\Delta NKM\cong\Delta KML\ \ \ \ \ \ AA$

$\Delta LKM\cong\Delta MNK\ \ \ \ \ \ \ \ SAS$

$\Delta LKM\cong\Delta KNM\ \ \ \ \ \ \ \ \ SSS$

19.

On a map the outline of the city is in a shape of the right trapezoid. The figure shows the measures of the city in miles of the boundaries given. The city has the population of 66,033 people. What is the population density in square mile of this city?

4 lines

20.

A swim course for athletes training in a triathlon is modeled in a coordinate plan where each unit represent 50 meters (m). What is the length of the swim course rounded with the near meter?

2033 m

2037 m

1992 m

1950 m

21.

On circle A CD is a diameter and point G lie on the circle. What is the measure of <G?

132

22.

“The set of all points that are a fixed distance from a given point” is the definition for which of the following terms?

Angle

Circle

Line segment

Ray

23.

In the figure below points H,D,C and G are on circle A as shown

· DI is a tangent on point D

· Point I lies outside of the circle such that <DIA=(2x +5)⁰

. <DAI= (8x + 5)⁰

What is measure in degrees of <HAG:

24.

Rectangle ACDG is shown in the coordinate plan below. Rectangle A’C’D’G’ is created applying the following sequence of transformation. Dilation of K=2 and center of dilation on point A followed by Rotation 90⁰ counterclockwise about the origin. Draw the rectangle A’C’D’G’

25.

What should be the best definition for thr reason 2?

Definition of similar triangles

Definition of congruent line segments

Opposite sides of the parallelograms are parallel

Opposite sides of the parallelogram are congruent.

26.

1. An equation is shown with angle measures expressed in degrees.

Cos 22=siny, 0 > y < 90. Enter the value of y in degrees.

a. 90

b. 78

c. 55

27.

Points A(-4,-3) and B(-1,5) are the endpoints of line segment AB. What ordered pair partitions line segment AB into a 1:3 ratio?

(-13/4, -1)

(-4/3, -1)

(-5/2, 1)

(-3, 15)

28.

Line segment FG is shown in the coordinate plan

Line IJ contains The point K(x,y) that partition IJ such that F and J are integers.

Select all of the possible ratios of FK:KJ

1:3

2:5

3:7

6:1

7:21

29.

Points A(-4,-3) and B(-1,5) are the endpoints of line segment AB. What ordered pair partition the line segment AB with the ratio of 1:3.

(-13/4, -1)

(-4/3, -1)

(-5/2, 1)

(-3, 15)

30.

Which statement is always true about the circle?

A circle is a polygon with no sides.

A circle is a polygon with one side.

All points of the circle are the same distance from a center.

All points of the circle are the same distance from any other point on a circle.

31.

Ashley construct triangle RST and XYZ, She determines that <S= 47⁰, <Y=51⁰, RS=XY and ST= YZ.

Based in this information, which comparison is true?

RT<XZ

RT > XZ

<R=<X

m<R< m<X

32.

A park has three paths forming a triangle. BD is 60m long and DA is 50m. Which inequality represent the length of path AB (z) in meters?

Z<10

0<Z<110

10<Z<110

Z>110

33.

A right triangle ABD is shown. The equation about the angles relationship is in the answer space. Put the letter that represent the angles in the right space

A, B, D

Sin_____=Cos______

4 lines

34.

John builds a scale model of a teepee for a history project. The dimensions of a teepee in inches are shown: What is the area in square inches of the base of the teepee. Round your answer to the nearest hundredth.

4 lines

35.

A science experiment call for a chemical solution that has a mass of 0.13 kilogram and a volume of 50 cubic centimeter What is the density of solution in grams per cubic centimeter?

4 lines

36.

Line P has the equation and line Q is parallel to p and cross the point (0,10). Write the equation of the line Q.

4 lines

37.

Circle O has the center (7,1), and a radius of 3 units. Circle M has the center (-8,-4) and the radius of 5 units. Which sequence of transformation can be performed on circle O to show that the circles are similar?

Translate the circle O with the rule: (X,Y)>>>>>>(X-15, Y-5) then dilate the result with scale of 3/5 with the center of dilation at point O’.

Translate the circle O with the rule: (X,Y)>>>>>>(X-15, Y-5) then dilate the result with scale of 5/3 with the center of dilation at point O’.

Translate the circle O with the rule: (X,Y)>>>>>>(X+15, Y+5) then dilate the result with scale of 3/5 with the center of dilation at point O’.

Translate the circle O with the rule: (X,Y)>>>>>>(X+15, Y+5) then dilate the result with scale of 5/3 with the center of dilation at point O’.

38.

Joseph prove that if two angles are supplementary to a third angle, then they are congruent to each other. Part of his proof is shown. Select the two words or phrases that complete the Joseph proof.

Assume that <1 and <2 are supplementary to <3. Therefore the <1 + <3=<2 + <3, each equal (a) (90⁰, 180⁰, 270⁰

39.

Joseph prove that if two angles are supplementary to a third angle, then they are congruent to each other. Part of his proof is shown. Select the two words or phrases that complete the Joseph proof.

Assume that <1 and <2 are supplementary to <3. Therefore the <1 + <3=<2 + <3, each equal_____________(90⁰, 180⁰, 270⁰By the transitive property of equality

m<1+ m<3=m<2 +m<3. Then eliminating m<3 on both sides by using _______________________( Transitive property, distributive property, reflexive property, substitution) resulting in m<1=m<2. Therefore by definition of congruence <1 and <2 must be congruent to each other.

(a)

40.

Rectangle ACDF with point D lying on AC and E and G lying on DF. Which equation correctly represents the relationship among the measures of the angles formed by the rectangle and segments BE and BG

Y=X-48

X=Z+41

Y+Z+48=X

X=48=

41.

Segments FG and F₁ G₁ Meets at point C and C’. FG AB in figure 2, but not in figure 1. D is a point lying at AB, and D’ lying at A₁B₁. Point D is reflected across the FG to create D’ and D₁is reflected across F₁G₁ to create D₁’. Select all the statements that should be true in both figures 1 and 2

2DC=DD’

2D₁C₁=D₁D₁’

D₁C₁=2C₁D₁’

Segment F₁ G₁ bisect D₁ D₁’

Segment FG bisect DD’

42.

Line AB and point C with the coordinates are shown in the coordinate plan below. What is the Y-intercept of the line parallel tom AB that contain the point C?

4 lines

43.

Circle O is circumscribed about the CDE. What is the measure of arc CD in degrees?

4 lines

44.

Mr Perera used two wooden board to make two triangular frames for displaying his insect collection. He originally planned to use three boards with the measures show in the ACD below. Since the 6 feet board was not available, he substituted 5 feet board as shown in EFG.1. Which statement is true when comparing ACD, the frame Mr Perera planned to build with EFG the one he built?

. m<A < m<G

m<D < m<E

m<C < m<G

m<C < m<F

45.

Maria has a roll of 50 pennies and a stack the 50 pennies. Her stack of pennies are leaning. Which is true about the volumes represented by the roll and by the stack of pennies?

The volume of the stack is slightly larger than the roll because the roll is leaning.

The volume of the roll is slightly larger than the stack because the roll is horizontal

Both volumes are the same, because there are the same numbers of pennies, and each penny has the same area.

The volumes can not be compare, because the volume of the roll can be represented as a cylinder.

46.

Which set of transformations also describes a rotation of any object?

A reflection of an object across one line followed by a reflection across a line parallel to the first line.

A translation of an object across one line followed by a translation across the line parallel to the first line.

A reflection of an object across one line followed by a reflection across a line perpendicular to the first line.

A translation of an object across one line followed by a reflection across a line perpendicular to the first line.

47.

A side view of the ramp at a miniature golf course is shown below:

Which of the following expressions can be use to find the distance a ball travels fro A to C in inches:

48.

Shayla is surveying and needs to find the width of the river at certain point. she selects the point B shows below, which is directly across the tree (point A), on the opposite side of the river. She measures AB at point C and places a rock there. She them measure <BCA. Using Shayla’s measurement, which equation can be use to find AB the width of the river in feet?

49.

AA Similarity

SSS Similarity

AAS Similarity

SAS Similarity

50.

In the diagram CD and CE are tangents of circle A at points D and E. Point B is on the circle and A is the center.The measure of the arc DBE is (200 + 2x)⁰. Which expression represent the measure of < DCE in terms of X?

(20 + 2x)⁰

(90-x)⁰

(100 + X)⁰

(160-2x)⁰

51.

1. Jack reflects the ABC across the line FQ to obtain the DBE as shown. Which statement Jack use to demonstrate that ABC = DBE:

52.

What value of x would prove that quadrilateral showm is a parallelogram?

53.

In order to complete the digging operation a group of archeologists used rope to hold up posts to block off a rectangular zone of land with side length of 42 feet and 60 feet as shown below. Later, they shortened the longer sides of this zone to make it an square. By how much did they shorten the perimeter of the digging zone?

54.

Peter pains a design of his bedroom wall. He sketches the design using a triangle and pentagon, where each grid box represents 1 square foot, as shown. What is the area of the design that Peter paints on his wall?

55.

The vertices of the Triangle ABC are (2,6), B(0,2), and C(3,3). What type of triangle is ABC

Equilateral

30-60-90 triangle

Scalene Triangle

45-45-90 Triangle

56.

Polygon PQRS has the vertices P(-3 , 2), Q(-2, 6), R(2,7), (1, 3):

Part A: What is the best classification of this polygon:

Parallelogram

Rhombus

Square

Kite

57.

Polygon PQRS has the vertices P(-3 , 2), Q(-2, 6), R(2,7), (1, 3):

Part B: What are the properties of this polygon. Select all that apply:

4 right angles

Diagonals are congruent

Diagonals bisect at 90⁰ angles.

Opposite angles are congruent.

Diagonal bisect the opposite angles

58.

Mary wants to know how the volume of the pyramid is related to the volume of the cube. She begins to partition the cube into six identical squares pyramids such that the base of each pyramid is made from the face of the cube as shown. Mary writes the expression 1/6(w/2)² to represent the volume of one of the six square pyramids, where w is the side length of the square base. Which statement is correct?

Mary did not make a mistake and the answer is correct.

Mary should have use w as w/2 resulting in the expression 1/6(w)³

Mary should have use a factor of 1/3 instead 1/6 resulting in the expression 1/3(w/2)³

Mary should have to square the term w/2 instead of cubing it, resulting in the expression 1/6(w/2)².

59.

The bench pictured was created from a rectangular block of wood. The original block measured 8 ft by 4ft by 4ft. What is the volume of the wooden bench in cubic feet?

128

96.75

31.25

88.7

60.

The figure below shows 5 congruent segments, each with endpoint A. Based in the angle measures which relationship among distances between endpoint can be stablish.

The distance between D and C’’ is greater than distance between C’’ and C

The distance between D and C’ is greater than distance between C’’’ and C.

The distance between C’’’ and C’ is greater than distance between C’’ and C’.

The distance between D and C’’ is greater than distance between C’’’ and C’.

61.

The developer is proposing to construct a new street that runs parallel to Creek Drive and intersects Lake Drive at (3,0). What is the equation of the line that will represents the new street?

y=-3x - 3

y=-3x + 9

y=1/3x - 1

y=1/3x + 3

62.

The bench pictured was created from a rectangular block of wood. The original block measured 8 ft by 4ft by 4ft. What is the volume of the wooden bench in cubic feet?

300

128

96.75

105

63.

Leah buys a jar of coconut oil. The jar contains 32.484 cubic inches of coconut oil. Which is the density of 0.033 pounds per cubic inches?

0.001

1086.732

984.36

1.0719

64.

An art supply store sell a cylindrical storage tube in two sizes. The smaller tube has a diameter of 12 centimeters and length of 14 centimeters. Each dimension of the larger tube is 25% greater of the same dimension of the smaller tube. How much is greater the volume of the greater tube than the volume of the smaller one?

360 cm³

810 cm³

832.5 cm³

1508.37cm³

65.

The figure below shows 5 congruent segments, each with endpoint A. Based in the angle measures which relationship among distances between endpoint can be stablish.

The distance between D and C’’ is greater than distance between C’’ and C

The distance between D and C’ is greater than distance between C’’’ and C.

The distance between C’’’ and C’ is greater than distance between C'' and C'

The distance between D and C’’ is greater than distance between C’’’ and C’.

66.

The developer is proposing to construct a new street that runs parallel to Creek Drive and intersects Lake Drive at (3,0). What is the equation of the line that will represents the new street?

y=-3x -3

y=-3x + 9

y=1/3x + 3

y=1/3x - 1

67.

A line segment has an endpoint at (4,10) and the other one at (16,0) What is the midpoint?

(5,10)

(3,3)

(10,5)

(5,5)

68.

A Pet store has 8 empty fish tank that hold 5544 cubic inches of water each. One goldfish require a a minimum of 1386 cubic inches of water. What is the greatest number of goldfish the pet store can have given thevolume of water needed for one goldfish?

$\frac{5544CI\ \ x\ 1386CI}{8}$

$\frac{8}{5544CI}\ x\ 1386CI$

$8CI\ x\ \frac{5544}{1386}$

$\frac{5544\ CI\ x\ 8}{1386\ CI}$

69.

The sculptor cut a block of ice for an ice sculpture along the dotted as shown: What cross section results from this cut?

70.

Quadrilateral SDUG has the vertices (1,5), (9,9), (11,5), (3,1), and diagonals intercept at (6,5). Select all the necessary steps to determine that the quadrilateral is a rectangle

Determine whether SU=DG

Determine whether SD=DU

Determine if the midpoint of SU is R

Determine if the midpoint of DG is R

Determine if SU and DG are perpendicular

71.

In the parallelogram KLMN m<N=(5x+10)⁰ and m<L=(8x-35)⁰

What is the m<K?

70⁰

85⁰

95⁰

110⁰

72.

The height of the pyramid is 12 units and the side length of the base is 10 units.

The cross section is an square with side length of 7.5 units.

The cross section is 2 times greater than the base

The cross section is 1.77 times less than the base.

The cross section is the same of the base.

The base is 10 times greater than the cross section.

73.

The company receive an order to create a rectangular prism using a metal. The metal has a density of 5 grams per cubic centimeter. Each prism has a mass of 320 grams. What are the possible dimensions of the rectangular prism in centimeters that this company should create

2cm x 6cm x 12cm

2cm x 4cm x 10cm

2cm x 4cm x 8cm

2cm x 5cm x 6cm

74.

Quadrilateral SDUG has the vertices (1,5), (9,9), (11,5), (3,1), and diagonals intercept at (6,5). Select all the necessary steps to determine that the quadrilateral is a rectangle

Determine whether SU=DG

Determine whether SD=DU

Determine if the midpoint of SU is R

Determine if the midpoint of DG is R

Determine if SU and DG are perpendicular

75.

The sculptor cut a block of ice for an ice sculpture along the dotted as shown: What cross section results from this cut?

76.

The circle is also divided into equal sections with the central angle of 40⁰. And the sectors are also rearranged as shown. The area of the sector is:

πr²/9

2πr/9

Πr²/3

9πr²

77.

The area of the sector with central angle of 40⁰ is:

36 times the area of the circle

1/9 the area of the circle

9 times the area of the circle

40 times the area of the circle

78.

The points (4,3), (0,0), and (4,0) are connected to create a two-dimensional polygon. What three-dimensional shape should be created by rotating the two-dimensional Polygon across the x-axis?

Cone

Cylinder

Pyramid

Triangular Prism.

79.

Rectangle ABCD with the center E has been created. Which transformation carries the rectangle onto itself:

Reflection across the line y=1.

Reflection across the line y=2x-3.

Rotation 90⁰ clockwise around the point E.

Rotation 180⁰clockwise around the point E.

80.

Which set of transformations also describes a rotation of any object?

A reflection of an object across one line followed by a reflection across a line parallel to the first line.

A translation of an object across one line followed by a translation across the line parallel to the first line

A reflection of an object across one line followed by a reflection across a line perpendicular to the first line.

A translation of an object across one line followed by a reflection across a line perpendicular to the first line.

81.

Cos 75⁰= $\frac{6}{AB}$

Cos 75⁰= $\frac{AB}{6}$

Tan 75⁰= $\frac{AB}{6}$

Tan 75⁰= $\frac{6}{AB}$

82.

(20 - 2x)⁰

(90-x)⁰

(100 + X)⁰

(160-2x)⁰

83.

A side view of the ramp at a miniature golf course is shown below:

Which of the following expressions can be use to find the distance a ball travels from A to C in inches:

$\frac{Cos25\degree}{24}$

$\frac{24}{Cos25\degree}$

$\frac{Sin\ 25\degree}{24}$

$\frac{24}{Sin\ 25\degree}$

84.

Ivis constructs triangle RST and XYZ, She determines that <S= 47⁰, <Y=51⁰, RS=XY and ST= YZ.

Based in this information, which comparison is true?

RT<XZ

RT > XZ

<R=<X

m<R< m<X

85.

Polygon PQRS has the vertices P(-3 , -2), Q(-2, 6), R(2,7), (1, 3): What is the best classification of this polygon:

Parallelogram

Rhombus

Sqauare

Kite

86.

Polygon PQRS has the vertices P(-3 , 2), Q(-2, 6), R(2,7), (1, 3): What are the properties of this polygon. Select all that apply:

Diagonals bisect to each other.

Diagonal bisect the opposite angles

Opposite angles are supplementary

4 right angles

Opposite sides are congruent and parallel

87.

Figure ABCD, to the right, is a parallelogram. What is the measure of∠𝐴𝐶𝐷?

59°

60°

61°

71°

88.

Given the diagram below, what is the value of x?

13.5

14.6

15.5

6.6

89.

In the diagram below, ∆𝐽𝐾𝐿 ≅ ∆𝑂𝑁𝑀.

Based on the angle measures in the diagram, what is the measure, in degrees, of ∠𝑁?

4 lines

90.

In ∆𝑆𝐶𝑈 shown below, points 𝑇 and 0 are on 𝑆𝑈̅̅ and 𝐶𝑈̅̅, respectively. Segment 𝑂𝑇̅ is drawn so that ∠𝐶 ≅ ∠𝑂𝑇𝑈. If 𝑇𝑈 = 4, 𝑂𝑈 = 5, and 𝑂𝐶 = 7, what is the length of 𝑆𝑇̅̅?

5.6

8.75

91.

In the diagram below, 𝐶𝐷̅̅ is the altitude drawn to the hypotenuse 𝐴𝐵̅̅ of right triangle 𝐴𝐵𝐶. Which lengths would not produce an altitude that measures 6√2?

𝐴𝐷 = 2 and 𝐷𝐵 = 36

𝐴𝐷 = 3 and 𝐴𝐵 = 24

𝐴𝐷 = 6 and 𝐷𝐵 = 12

𝐴𝐷 = 8 and 𝐴𝐵 = 17

92.

To find the height of a lamppost at a park, Rachel placed a mirror on the ground 20 feet from the base of the lamppost. She then stepped back 4 feet so that she could see the top of the lamp post in the center of the mirror. Rachel's eyes are 5 feet 6 inches above the ground. What is the height, in feet, of the lamppost?

4 lines

93.

. In right triangle ABC, 𝑚∠𝐵 ≠ 𝑚∠𝐶. Let sin𝐵 = 𝑟 and cos𝐵 = 𝑠 . What is sin𝐶 − cos 𝐶?

𝑟 + 𝑠

𝑟 − 𝑠

𝑠 – 𝑟

𝑟/s

94.

Erin is buying produce at a store. She buys c cucumbers at $0.99 each and a apples at $0.79 each. Write the expression for this situation

0.99a + 0.79a

0.99c + 0.79a

0.99a + 0.79c

0.99c + 0.79c

95.

The number of bees that visit a plant is 500 times the number of years the plant is alive, where t represents the number of years the plant is alive. Write the expression for this situation.

500

1000

500t

96.

Lorenzo buys 3 shirts at s dollars apiece and 2 pairs of pants at p dollars a pair. What does the expression represent?

6s + 2p

2s + 3p

3s + 2p

3p + 2s

97.

If a car travels at a speed of 25 mi/h for t hours, then travels 45 mi/h for m hours. Write the expression for this situation.

25t + 45m

25m + 45t

45t + 25m

25t + 45t

98.

99.

100.

101.

102.

103.

104.

105.

106.

107.

A 30-foot long escalator forms a 41° angle at the second floor. Which is the closest height of the first floor?

20 feet

22.5 feet

24.5 feet

26 feet

108.

Jane and Mark each build ramps to jump their remote-controlled cars. Both ramps are right triangles when viewed from the side. The incline of Jane's ramp makes a 30-degree angle with the ground, and the length of the inclined ramp is 14 inches. The incline of Mark's ramp makes a 45-degree angle with the ground, and the length of the inclined ramp is 10 inches.

What is the horizontal length of the base of Jane's ramp and the base of Mark's ramp?

4 lines

109.

Which car is launched from the highest point?

4 lines

110.

In ∆𝐴𝐵𝐶, the complement of ∠𝐵 is ∠𝐴. Which statement is always true?

𝑡𝑎𝑛 ∠𝐴 = 𝑡𝑎𝑛 ∠𝐵

𝑠𝑖𝑛 ∠𝐴 = 𝑠𝑖𝑛 ∠𝐿𝐵

𝑐𝑜𝑠∠𝐴 = 𝑡𝑎𝑛 ∠𝐵

𝑠𝑖𝑛 ∠𝐴 = 𝑐𝑜𝑠 ∠B

111.

The diagram below shows a ramp connecting the ground to a loading platform 4.5 feet above the ground. The ramp measures 11.75 feet from the ground to the top of the loading platform.

Determine and state, to the nearest degree, the angle of elevation formed by the ramp and the ground

4 lines

112.

As shown in the diagram below, the angle of elevation from a point on the ground to the top of the tree is 34°. If the point is 20 feet from the base of the tree, what is the height of the tree, to the nearest tenth of a foot?

29.7

16.6

3.5

11.2

113.

What is the sine ratio of ∠𝑃 in the given triangle?

8/17

8/15

15/17

5/8

114.

Kendall drew a right triangle. The tangent value for one angle in her triangle is 1.8750. Which set of side lengths could belong to a right triangle similar to the triangle Kendall drew?

16 cm, 30 cm, 35 cm

8 cm, 15 cm, 17 cm

16 cm, 8 cm, 10 cm

1.875 cm, 8 cm, 8.2 cm

115.

Triangle ABC is similar to triangle WYZ. Select all angles whose tangent equals 3/4 .

∠A

∠B

∠C

∠W

∠Y

116.

The figure shows right ∆𝐴𝐵𝐶. Of the listed values are equal to the sine of 𝐵? Select ALL that apply.

b/c

c/a

b/a

The cosine of C

The sine of (90° − 𝐶)

117.

Which is equal to 𝑠𝑖𝑛 30°?

cos 30°

cos 60°

sin 60°

sin 70°

118.

Adnan states if 𝑐𝑜𝑠30° ≈ 0.866, then 𝑠𝑖𝑛30° ≈ 0.866. Which justification correctly explains whether or not Adnan is correct?

Adnan is correct because 𝑐𝑜𝑠𝑥° and 𝑠𝑖𝑛𝑥° are always equivalent in any right triangle.

Adnan is correct because 𝑐𝑜𝑠𝑥° and 𝑠𝑖𝑛𝑥° are only equivalent in a 30° − 60° − 90° triangle.

Adnan is incorrect because 𝑐𝑜𝑠𝑥° and 𝑠𝑖𝑛(90 − 𝑥)° are always equivalent in any right triangle.

Adnan is incorrect because only 𝑐𝑜𝑠𝑥° and 𝑐𝑜𝑠(90 − 𝑥)° are equivalent in a 30°-60°-90° triangle.

119.

In the diagram below, transversal 𝑇𝑈⃡ intersects 𝑃𝑄⃡ and 𝑅𝑆⃡ at 𝑉 and 𝑊, respectively. If 𝑚∠𝑇𝑉𝑄 = 5𝑥 − 22 and 𝑚∠𝑇𝑉𝑄 = 3𝑥 + 10, for which value of 𝑥 is 𝑃𝑄⃡ ∥ 𝑅𝑆, ⃡ ?

120.

Peach Street and Cherry Street are parallel. Apple Street intersects them, as shown in the diagram below.

If 𝑚∠1 = 2𝑥 + 36 and 𝑚∠2 = 7𝑥 − 9, what is 𝑚∠1?

121.

In the diagram below of isosceles triangle ABC, 𝐴𝐵̅̅ ≅ 𝐶𝐵̅̅ and angle bisectors 𝐴𝐷̅, 𝐵𝐹̅̅, and 𝐶𝐸̅ are drawn and intersect at 𝑋. If 𝑚∠𝐵𝐴𝐶 = 50°, find 𝑚∠𝐴𝑋𝐶. 𝑚∠𝐴𝑋𝐶 = 130°

𝑚∠𝐴𝑋𝐶 = 30°

𝑚∠𝐴𝑋𝐶 = 130°

𝑚∠𝐴𝑋𝐶 = 190°

𝑚∠𝐴𝑋𝐶 = 250⁰

122.

What is the measure of ∠𝐵 in the figure below?

62°

58°

59°

56°

123.

In this figure, 𝒍||𝒎. Jessie listed the first two steps in a proof that ∠𝟏 + ∠𝟐 + ∠𝟑 = 𝟏𝟖𝟎°. Which justification can Jessie give for Steps 1 and 2?

Vertical angles are congruent

Corresponding angles are congruent.

Alternate interior angles are congruent.

Alternate exterior angles are congruent

124.

Which of these is the most logical order for the statements and reasons?

I, II, III, IV, V

III, II, V, I, IV

III, II, V, IV, I

II, V, III, IV, I

125.

𝑌𝑄̅̅ and 𝑋𝑃̅̅ are altitudes to the congruent sides of isosceles triangle 𝑊𝑋𝑌. Keisha is going to prove ̅𝑌𝑄̅̅ ≅ 𝑋𝑃̅̅ by showing they are congruent parts of the congruent triangles 𝑄𝑋𝑌 and 𝑃𝑌X

AAS - because triangle 𝑊𝑋𝑌 is isosceles, its base angles are congruent. Perpendicular lines form right angles, which are congruent; and segment 𝑋𝑌̅̅ is shared.

AAS - because triangle 𝑊𝑋𝑌 is isosceles, its base angles are congruent. Perpendicular lines form right angles, which are congruent; and segment 𝑋𝑌̅̅ is shared. B. SSS - because segment 𝑄𝑃̅̅ would be parallel to segment 𝑋𝑌̅̅.

SSA - because segment 𝑋𝑌̅ is shared; segments 𝑋𝑃̅̅ and ̅𝑌𝑄̅̅ are altitudes, and 𝑊𝑋𝑌 is isosceles, so base angles are congruent.

ASA - because triangle 𝑊𝑋𝑌 is isosceles, its base angles are congruent. Segment 𝑋𝑌̅̅ is shared; and perpendicular lines form right angles, which are congruent.

126.

In the diagram below, 𝐷𝐸̅̅,𝐷𝐹̅̅, and ̅𝐸𝐹̅̅are midsegments of ∆𝐴𝐵𝐶.

The perimeter of quadrilateral 𝐴𝐷𝐸𝐹 is equivalent to:

𝐴𝐵 + 𝐵𝐶 + 𝐴𝐶

1 /2 𝐴𝐵 + 1/ 2 𝐴𝐶

2𝐴𝐵 + 2𝐴𝐶

𝐴𝐵 + 𝐴C

127.

Two pairs of parallel line form a parallelogram. Becki proved that angles 2 and 6 are congruent. She is first used corresponding angles created by a transversal and then alternate interior angles. Which pairs of angles could she use?

1 and 2 then 5 and 6

4 and 2 then 4 and 6

7 and 2 then 7 and 6

8 and 2 then 8 and 6

128.

To prove that diagonals of a parallelogram bisect each other, Xavier first wants to establish that triangles APD and CPB are congruent. Which criterion and elements can he use?

SAS: sides AP & PD and CP & PB with the angles in between

SAS: sides AD & AP and CB & CP with the angles in between

ASA: sides DP and PB with adjacent angles

ASA: sides AD and BC with adjacent angles

129.

In the diagram below of parallelogram 𝑆𝑇𝑈𝑉, 𝑆𝑉 = 𝑥 + 3, 𝑉𝑈 = 2𝑥 − 1, and

𝑇𝑈 = 4𝑥 − 3.

What is the length of 𝑆𝑉̅̅?

130.

The figure shows parallelogram 𝐴𝐵𝐶𝐷 with 𝐴𝐸 = 18.

Let 𝐵𝐸 = 𝑥 2 − 48 and let 𝐷𝐸 = 2𝑥 . What are the lengths of ̅𝐵𝐸̅̅ and 𝐷𝐸̅̅?

4 lines

131.

Step 1

Step 2

Step 3

tep 4

132.

The figure shows parallelogram PQRS on a coordinate plane. Diagonals 𝑆𝑄̅̅ and 𝑃𝑅̅̅ intersect at point 𝑇.

Find the coordinates of point Q in terms of a, b, and c.

4 lines

133.

Parallelogram 𝐴𝐵𝐶𝐷 has coordinates 𝐴(0,7) and 𝐶(2,1). Which statement would prove that 𝐴𝐵𝐶𝐷 is a rhombus?

The midpoint of 𝐴𝐶̅̅ is (1,4).

The length of 𝐵𝐷̅̅ is √40.

The slope of 𝐵𝐷̅̅ is 1/3

The slope of 𝐴𝐵̅̅̅̅ is 1/3

134.

Which transformation will place the trapezoid onto itself?

counterclockwise rotation about the origin by 90°

rotation about the origin by 180°

reflection across the x-axis

reflection across the y-axis

135.

Which transformation will carry the rectangle shown below onto itself

a reflection over line m

a reflection over the line 𝑦 = 1

a rotation 90° counterclockwise about the origin

a rotation 270° counterclockwise about the origin

136.

Which figure has 90° rotational symmetry?

A. Square

Regular hexagon

Regular pentagon

Equilateral triangle

137.

Which rotation about its center will carry a regular decagon onto itself?

54°

162°

198°

252°

138.

It is known that a series of rotations, translations, and reflections superimposes sides a, b, and c of Quadrilateral X onto three sides of Quadrilateral Y. Which is true about z, the length of the fourth side of Quadrilateral Y?

It must be equal to 6

It can be any number in the range 5 ≤ 𝑧 ≤ 7

It can be any number in the range 3 ≤ 𝑧 ≤ 8

It can be any number in the range 0 < 𝑧 < 14

139.

Which transformation will always produce a congruent figure?

(𝑥 ′ , 𝑦 ′ ) → (𝑥 + 4, 𝑦 − 3)

(𝑥 ′ , 𝑦 ′ ) → (2𝑥, 𝑦)

(𝑥 ′ , 𝑦 ′ ) → (𝑥 + 2, 2𝑦)

(𝑥 ′ , 𝑦 ′ ) → (2𝑥, 2𝑦)

140.

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

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

141.

The image of ∆𝐴𝐵𝐶 after a rotation of 90° clockwise about the origin is ∆𝐷𝐸𝐹, as shown below

Which statement is true?

𝐵𝐶̅̅ ≅ 𝐷𝐸̅̅

𝐴𝐵̅̅ ≅ 𝐷𝐹̅̅

∠𝐶 ≅ ∠𝐸 D.

∠𝐴 ≅ ∠𝐷

142.

If ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹, which segment is congruent to 𝐴𝐶̅̅̅̅?

𝐷𝐸̅̅

𝐸𝐹̅̅

𝐷𝐹̅̅

𝐴B

143.

Given the information regarding triangles ABC and DEF, which statement is true?

The given information matches the SAS criterion; the triangles are congruent.

The given information matches the ASA criterion; the triangles are congruent.

Angles C and F are also congruent; this must be shown before using the ASA criterion.

It cannot be shown that the triangles are necessarily congruent.

144.

Which statements should be used to prove that the measures of angles 1 and 5 sum to 180°?

Angles 1 and 8 are congruent as corresponding angles; angles 5 and 8 form a linear pair.

Angles 1 and 2 form a linear pair; angles 3 and 4 form a linear pair.

Angles 5 and 7 are congruent as vertical angles; angles 6 and 8 are congruent as vertical angles.

Angles 1 and 3 are congruent as vertical angles; angles 7 and 8 form a linear pair.

145.

Which statement justifies why the constructed line passing through the given point A is parallel to 𝐶𝐷̅̅̅̅?

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.

146.

. Let's say you opened your laptop and positioned the screen so it's exactly at 90°—a right angle—from your keyboard. Now, let's say you could take the screen and push it all the way down beyond 90°, until the back of the screen is flat against your desk. It looks as if the angle disappeared, but it hasn't. What is the angle called, and what is its measurement?

Straight angle at 180°

Linear angle at 90°

Collinear angle at 120°

Horizontal angle at 180°

147.

What is defined below? __________: a portion of a line bounded by two points

arc

axis

ray

segment

148.

Given 𝑋𝑌⃡ and ⃡𝑍𝑊 intersect at point 𝐴. Which conjecture is always true about the given statement?

𝑋𝐴 = 𝐴𝑌

∠𝑋𝐴𝑍 is acute.

𝑋𝑌⃡ is perpendicular to ⃡𝑍𝑊

𝑋, 𝑌, 𝑍, and 𝑊 are noncollinear

149.

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

150.

A transformation takes point A to point B. Which transformation(s) could it be?

F only

F and R only

F and T only

F, R, and T

151.

The point (−7,4) is reflected over the line 𝑥 = −3. Then, the resulting point is reflected over the line 𝑦 = 𝑥. Where is the point located after both reflections?

(−10, −7)

(1, 4)

(4, −7)

(4, 1)

152.

Given: 𝐴𝐵̅with coordinates of 𝐴(−3, −1) and 𝐵(2, 1) 𝐴̅B with coordinates of

𝐴 ′ (−1, 2) and 𝐵 ′ (4,4) Which translation was used?

(𝑥 ′ , 𝑦 ′ ) → (𝑥 + 2, 𝑦 + 3)

(𝑥 ′ , 𝑦 ′ ) → (𝑥 + 2, 𝑦 − 3)

(𝑥 ′ , 𝑦 ′ ) → (𝑥 − 2, 𝑦 + 3)

(𝑥 ′ , 𝑦 ′ ) → (𝑥 − 2, 𝑦 − 3)

153.

Point P is located at (4, 8) on a coordinate plane. Point P will be reflected over the x-axis. What will be the coordinates of the image of point P?

(−8, 4)

(−4, 8)

(4, −8)

(8, 4)

154.

Point 𝐹′ is the image when point 𝐹 is reflected over the line 𝑥 = −2 and then over the line 𝑦 = 3. The location of 𝐹′ is (3, 7). Which of the following is the location of point 𝐹?

(−7, −1)

(−7, 7)

(1, 5)

(1, 7)

155.

∆𝐽𝐾𝐿 is rotated 90° about the origin and then translated using

(𝑥, 𝑦) → (𝑥 − 8, 𝑦 + 5). What are the coordinates of the final image of point 𝐿 under this composition of transformations?

(−7, 10)

(−7, 0)

(−9, 10)

(−9, 0)

156.

The graph of a figure and its image are shown below. Identify the transformation to map the image back onto the figure.

Reflection

Rotation

Translation

Dilation

157.

The graph of a figure and its image are shown below. Identify the transformation to map the image back onto the figure.

Reflection

Rotation

Translation

Dilation

158.

If triangle ABC is rotated 180 degrees about the origin, what are the coordinates of A′?

(4,5)

(5,-4)

(-5,-4)

(-4,-5)

159.

What is the image of 𝑀(11, −4) using the translation (𝑥, 𝑦) → 𝑥 − 17, 𝑦 + 2?

𝑀′ (−6, −2)

𝑀′ (6, 2)

𝑀′(−11, 4)

𝑀′(−4, 11)

160.

Which transformation maps the solid figure onto the dashed figure?

rotation 180° about the origin

translation to the right and down

reflection across the x-axis

reflection across the y-axis

161.

What is the x intercept of the line?

(a)

162.

What is the equation of the line?

(a)

163.

What is the equation of a line perpendicular to this line?

Use b as any y-intercept.

(a)

164.

What is the equation of a line parallel to this line, that cross the point (-4,-1)?

(a)

165.

What is the equation of a line perpendicular to this line and cross the point (1,2)

(a)

166.

Which of the following ordered pair could represent a y-intercept on a graph? (6, 0),(0, 4),(-1, 3),(2, 0).

(a)

167.

Give the y-interecept for this equation

3x + y = 5

(a)

168.

Give the x-intercept

3x + 8y = 24

(a)

169.

What equation corresponds to the following graph?

(a)

170.

What is the solution of this equation system?

(a)

171.

Find the solution of this equation system

y = 2x + 1

y = 4x - 1

(a)

172.

What is the best method you would use to find the solution of this equation system

y = 2x + 1

y = 4x - 1

(a)

173.

If you use the method "multiplying first" what is the first step solving the following equation system?

y = 2x + 1

y = 4x - 1

(a)

174.

What are the factors of the following quadratic equation?

b² -7b - 8

(a)

175.

What are the factors of the following quadratic equation?

x² + 10x + 9

(a)

176.

Which type of line should be the following inequalities?

5 ≥ x

(a)

177.

Write the linear inequality

(a)

178.

Are the points on the line part of the solution set or not?

(a)

179.

Write the the following inequality

(a)

180.

Where will be the shade area of the following inequality?

y< -x + 4

(a)

Reset

Review EOC Geometry Grade 10 Mathematics

Total questions: 180

Worksheet time: 2hrs 31mins

Similar Resources on Wayground