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Geometry Quarter 1 Practice Test

Total questions: 105

Worksheet time: 3hrs 23mins

Name
Class
Date
1.

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)

e)

Not enough information to write a rule.

2.

Identify the transformation from ABC to A'B'C'.

a)

90o clockwise rotation

b)

90o counter clockwise rotation

c)

Reflection across the y-axis

d)

Reflection across the x-axis

e)

Translation down 2 units

3.

Identify the transformation from ABCD to A'B'C'D'.

a)

Translation (x,y) -->(x-7,y)

b)

Reflection across the y-axis

c)

Reflection across the x-axis

d)

90o counter clockwise Rotation

e)

Translation (x,y) --> (x+7, y)

4.

Identify the transformation from A to D.

a)

90o Clockwise Rotation

b)

180o Rotation

c)

270o Clockwise Rotation

d)

Y-Axis Reflection

e)

X-Axis Reflection

5.

Which rule would dilate shows a scale factor of 4

a)

(x, y) → (y, x)

b)

(x, y) → (x + 4, y + 4)

c)

(x, y) → (x - 4, y -4)

d)

(x, y) → (4x, 4y)

e)

(x, y) → (1/4x, 1/4y)

6.

What is the rule for the dilation pictured below?

a)

(x, y) → (½x, ½y)

b)

(x, y) → (x + 2, y + 2)

c)

(x, y) → (2x, 2y)

d)

(x, y) → (2x, 3y)

e)

(x, y) → (1/3x, 1/3y)

7.

What is the sequence of transformations?

a)

Reflect over the y then reflect over the x

b)

Reflect over the x then reflect over the y

c)

Translate 4 units then rotate 90˚

d)

Rotate 90˚ then reflect over the x

e)

Rotation of 180 degrees

8.

Which of the following describes the sequence of transformations shown?

a)

Reflect across the x-axis and then rotate -90 (clockwise) around the origin

b)

Rotate -90 (clockwise) 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 (counterclockwise) degrees about the origin.

e)

Y-Axis reflection and then a x-axis reflection.

9.

What types of transformations happened to get from shape 1 to shape 3, choose ALL that apply.

a)

Rotation

b)

Translation

c)

Reflection

d)

Dilation

e)

Non-Rigid Transformation

10.

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)

e)

(-6,4)

11.

Choose the correct transformations

a)

rotate 90 degrees counter-clockwise around the origin, and then reflect over the x-axis

b)

right 1, down 4, and then reflection over the y-axis

c)

right 6, and then reflection over the x-axis

d)

reflection over the line y=x, and then translate up 4, right 2

e)

reflection over the y-axis, and then (x,y) --> (x-1, y+4)

12.

Choose the correct transformations

a)

rotate 90 degrees counter-clockwise around the origin, and then reflect over the x-axis

b)

right 1, down 4, and then reflection over the y-axis

c)

right 6, and then reflection over the x-axis

d)

reflection over the line y=x, and then translate up 4, right 2

e)

reflection of the x-axis, and then a translation to the left 6

13.

Choose the correct transformations

a)

rotate 90 degrees counter-clockwise around the origin, and then reflect over the x-axis

b)

right 1, down 4, and then reflection over the y-axis

c)

right 6, and then reflection over the x-axis

d)

reflection over the line y=x, and then translate up 4, right 2

e)

reflection over the x-axis, and then rotate 90 degrees clockwise around the origin

14.

Describe the transformations that map ABC onto A"B"C"

a)

translate 5 up and 1 left then reflect over y

b)

translate 5 down and 1 left, then reflect over y

c)

reflect over y=x then translate left 8

d)

reflect over x then rotate 90 clockwise

e)

reflect over the x-axis then translate 4 to the right

15.

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

e)

reflect over y then right 6 down 1

16.

Choose the correct scale factor:

a)

2

b)

3

c)

1/3

d)

1/2

e)

Not enough Information

17.

What is the rule for the following reflection?

a)

Reflection across y = −2

b)

Reflection across x = −2

c)

Reflection across x = 2

d)

Reflection across y = 2

e)

Reflection across y = x

18.

Identify the smallest angle of rotation that maps the image to itself.

a)

180°

b)

360°

c)

90°

d)

No rotational symmetry

e)

72°

19.

The rule for dilation is

(x, y) --> _

a)

(kx, ky)

b)

(x, -y)

c)

(-x, y)

d)

(x+a, y+b)

e)

(-x,-y)

20.

The rule for reflection over the x-axis is

(x, y) --> _

a)

(-x, y)

b)

(x, -y)

c)

(y, x)

d)

(-y, -x)

e)

(-x,-y)

21.

The rule for rotation of 180 degrees is

(x, y) --> _

a)

(-y, x)

b)

(-x, -y)

c)

(y, -x)

d)

(-y, -x)

e)

(-x, y)

22.

Which rule describes the action of the coordinates when a figure is reflected over the line y = x?

a)

(x, y)→(-y, -x)

b)

(x, y)→(-x, y)

c)

(x, y)→(-x, -y)

d)

(x, y)→(y, x)

e)

(x, y)→(-y, x)

23.

A transformation that does not change the size or shape of a pre-image (pre-image and image are congruent) is called

a)

Rigid Motion Transformation

b)

Dilation

c)

Non-Isometric

d)

Non- Rigid Motion Transformation

e)

Similar Figure Transformation

24.

Which is NOT an Isometry?

a)

Relection

b)

Dilation

c)

Rotation

d)

Translation

e)

Not Enough Information

25.

Identify the smallest angle of rotation that maps the image to itself.

a)

90°

b)

180°

c)

45°

d)

60°

e)

30°

26.

A rigid motion creates figures that are ____________.

a)

congruent

b)

different sizes

c)

similar

d)

larger

e)

dilated figures

27.

What are the series of rigid motions that would map ∆ABC onto ∆A''B''C''?

a)

a reflection followed by a rotation

b)

a reflection followed by a translation

c)

a translation followed by a rotation

d)

a translation followed by a reflection

e)

a rotation followed by a translation

28.

Which of the following transformation will map the regular pentagon onto itself, choose ALL that apply?

a)

x axis reflection

b)

y axis reflection

c)

90 degree rotation

d)

180 degree rotation

e)

72 degree rotation around the orgin

29.

Which of the following transformation will map the trapezoid onto itself, choose ALL that apply?

a)

x axis reflection

b)

reflection across green line

c)

rotation 90 degrees about (2,-1)

d)

reflection across the blue line

e)

rotation 180 degrees about (2,-1)

30.

Which of the following transformation will map the regular pentagon onto itself?

a)

reflection across blue line

b)

reflection across green line

c)

108 degree rotation about the origin

d)

216 degree rotation about the origin

e)

None of the transformation map onto the original penatgon

31.

Which transformation will map the rectangle onto itself?

a)

90 degree rotation about (-2,1)

b)

540 degree rotation about (-2,1)

c)

reflection across the x axis

d)

reflection across the blue line

e)

reflection across the x axis

32.

Which of the following transformations will NOT map the regular hexagon onto itself?

a)

270 degree rotation about the origin

b)

x axis reflection

c)

y axis reflection

d)

180 degree rotation about the origin

e)

120 degree rotation about the origin

33.

Which transformation will map the parallelogram onto itself?

a)

reflection x axis

b)

reflection y axis

c)

refection across the green line

d)

reflection over the line y=x

e)

none of these above

34.

A straightedge and compass were used to creat the construction above. Arc EF was drawn from Point B, and arcs with equal radii were drawn from E and F. Choose all of the following that must be true.

a)
b)
c)
d)
35.

Based on the construction above which of the following are always true, choose all that apply.

a)
b)

AB=CD

c)

AE=EB

d)

CE=ED

e)

AC=BC

36.

Name the construction.

a)

Corresponding angles

b)

Parallel line to a point not on the line

c)

Perpendicular line to a point not on the line

d)

Angle bisector

e)

Alternate Interior Angles

37.

Name the construction.

a)

Midpoint

b)

Perpendicular through a point on the line

c)

Perpendicular through a point NOT on the line

d)

Circumcenter of a right triangle

e)

Constructing the center of the circle on the y-axis

38.
a)

A line perpendicular to one of two parallel lines is perpendicular to the other.

b)

Two lines are perpendicular if they intersect to form congruent adjacent angles.

c)

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

d)

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

e)

When two lines are intersected by a traversal and same side exterior angles are congruent, the lines are parallel.

39.

Which of the following is the construction of an equilateral triangle given side AB?

a)
b)
c)
d)
e)

Not enough information without labeled side lengths

40.

Name the pictured construction.

a)

Circled Hexagon

b)

Hexagon Inscribed in a Circle

c)

Square Inscribed in a Circle

d)

Triangle Inscribed in a Circle

e)

Circumscribed Polygon with an Inscribed Circle

41.

The following shows the steps of which construction?

a)

inscribed triangle

b)

inscribed hexagon

c)

circumscribed square

d)

inscribed square

e)

circumscribed rhombus

42.

Becky leaves school to go home. She walks 6 blocks North and then 8 blocks west. How far is Becky from the school?

a)

14 blocks

b)

12 blocks

c)

10 blocks

d)

8.5 blocks

e)

13 blocks

43.

Choose all pairs of vertical angles?

a)

∠COB & ∠COA

b)

∠AOD & ∠AOC

c)

∠COB & ∠AOD

d)

∠BOD & ∠AOD

e)

∠COA & ∠BOD

44.

What is the value of x?

a)

37

b)

72

c)

108

d)

18

e)

74

45.

Find the value of x.

a)

74

b)

37

c)

52

d)

105

e)

75

46.

What is the relationship of the two angles shown in the picture and what is the value of x.

a)

Complementary; x=3.4

b)

Complementary; x=45

c)

Supplementary; x=20

d)

Supplementary; x=175

e)

Vertical Angles x= -5

47.

Identify all the correct statement.

a)

∠1 & ∠2

are corresponding angles

b)

∠2 & ∠4

are vertical angles

c)

∠5 & ∠8

are vertical angles

d)

∠1 & ∠5

are corresponding angles

e)

∠4 & ∠5

are alternate exterior angles

48.

What are lines that intersect to make a right angle?

a)

perpendicular

b)

complementary

c)

supplementary

d)

corresponding

e)

parallel

49.

What are line segments or angles that have the same measure?

a)

perpendicular

b)

parallel

c)

congruent

d)

ray

e)

similar

50.

What are lines in a plane that do not intersect?

a)

skew

b)

parallel

c)

perpendicular

d)

transversal

e)

straight

51.

Find the measure of the missing angle.

a)

72 degrees

b)

108 degrees

c)

18 degrees

d)

90 degrees

e)

36 degrees

52.

The Triangle Sum Theorem states that the sum of the angles of a triangle equal how many degrees?

a)

90

b)

360

c)

150

d)

180

e)

60

53.

What do we call a triangle with three different side lengths?

a)

scalene

b)

isosceles

c)

equilateral

d)

Pythagorean Theorem

e)

obtuse

54.

What do we call a triangle with two equal sides and angles?

a)

scalene

b)

isosceles

c)

equilateral

d)

Pythagorean Theorem

e)

obtuse

55.

What do we call a triangle with three equal sides

a)

scalene

b)

obtuse

c)

equilateral

d)

right

e)

isosceles

56.

What is the value of b:

a)

146

b)

34

c)

36

d)

115

e)

31

57.

Supplementary angles equal what?

a)

45 degrees

b)

360 degrees

c)

180 degrees

d)

90 degrees

e)

60 degrees

58.

Equilateral Triangle

a)

2 sides that are equal; 2 equal angles

b)

No sides are equal; no equal angles

c)

All 3 angles measure less than 90 degrees

d)

All 3 sides are equal; all angles equal 60 degrees

e)

2 equal base angles; no equal sides

59.

What type of triangle is this?

a)

Equilateral

b)

Isosceles

c)

Scalene

d)

Obtuse

e)

Equal-angular

60.

What type of triangle is this, choose all that apply?

a)

Equilateral Triangle

b)

Scalene Triangle

c)

Isosceles Triangle

d)

Right Triangle

e)

Acute Triangle

61.

Given triangle JKL what is the measure of angle L?

a)

9 degrees

b)

25 degrees

c)

47 degrees

d)

52 degrees

e)

108 degrees

62.

What is the value of x?

a)

60 degrees

b)

5 degrees

c)

10 degrees

d)

15 degrees

e)

30 degrees

63.

What is the value of (?)

a)

90 degrees

b)

80 degrees

c)

70 degrees

d)

60 degrees

e)

40 degrees

64.

What is the value of x?

a)

20o

b)

60o

c)

15o

d)

40o

e)

8 in.

65.

What is the measure of angle 2?

a)

50 degrees

b)

57.5 degrees

c)

65 degrees

d)

115 degrees

e)

180 degrees

66.
a)
b)
c)
d)
67.

Triangle ABC has been reflected to form DFE. If ∠C is 40o find the measure of ∠F.

a)

40o

b)

50o

c)

90o

d)

45o

e)

140o

68.

How many lines of symmetry does the picture have?

a)

0 lines of symmetry

b)

1 line of symmetry

c)

2 lines of symmetry

d)

3 lines of symmetry

e)

Not enough information

69.

Which would be the best classification for the triangle shown?

a)

right isosceles

b)

obtuse scalene

c)

obtuse isosceles

d)

acute scalene

e)

equilateral

70.

Classifying the following the triangle as many ways as possible.

a)

Acute, Scalene

b)

Right, Scalene

c)

Obtuse, Scalene

d)

Acute, Isosceles

e)

Obtuse, Isosceles

71.

Which one is the easy way to remember trigonometric ratios?

a)

Sah Coh Toa

b)

Soh Cah Toa

c)

Soh Cah Tao

d)

Soh Cah Toh

e)

Sah Coa Toh

72.

If you are given the hypotenuse and an adjacent side, which trigonometric function should you use to find the angle?

a)

sine

b)

cosine

c)

tangent

d)

cotangent

e)

Pythagorean theorem

73.

We can use SOH-CAH-TOA for...

a)

Any triangle ever

b)

Non-right triangles only

c)

Right Triangles only

d)

Never

e)

Classifying Triangles

74.

Which method?

a)

45-45-90 Triangle

b)

30-60-90 Triangle

c)

Trig (SOHCAHTOA)

d)

Pythagorean Theorem

e)

Inverse Trig (SOHCAHTOA)

75.

Find Cos(A) as a decimal rounded the the nearest ten-thousandth.

a)

.4706

b)

1.875

c)

.8824

d)

.5333

e)

61.92

76.

Find Tan A

a)

21/20

b)

29/20

c)

21/29

d)

20/21

e)

20/29

77.

What is cos(B)?

a)

a/c

b)

b/c

c)

a/b

d)

b/a

e)

c/a

78.

What is sin(B)?

a)

a/c

b)

b/c

c)

a/b

d)

b/a

e)

c/a

79.

Choose the correct ratio.

a)

cos(33)=x/14

b)

sin(33)=x/14

c)

cos(33)=14/x

d)

sin(33)=14/x

e)

tan(33)=14/x

80.

Set up the problem...

a)

sin X = 41/28

b)

tan X = 41/28

c)

cos X = 28/41

d)

sin X = 28/41

e)

tan X = 28/41

81.

Based on the diagram, choose all the statements that are true.

a)
b)
c)
d)
e)
82.

Right triangle ABC is shown below. Which equation gives the correct value for BC?

a)
b)
c)
d)
e)

Not enough information to solve BC

83.

Find the measure of the missing angle.

a)

49o

b)

50o

c)

41o

d)

33o

e)

57o

84.

Which trigonometric ratios are correct?

a)

cos C= adj/hyp

b)

sin C= adj/hyp

c)

tan C= adj/hyp

d)

tan C=adj/opp

e)

tan C= opp/adj

85.

Find h

a)

35.60

b)

45.57

c)

35.71

d)

61.03

e)

44.43

86.

Find the length of the missing side.

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

e)

10.9 cm

87.

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

a)

17 miles

b)

32 miles

c)

37 miles

d)

40 miles

e)

42 miles

88.

A rectangular field is 50 yards wide and 100 yards long. Patrick walks diagonally across the field. How far does he walk?

a)

111.8 yards

b)

115 yards

c)

127.3 yards

d)

119 yards

e)

86.6 yards

89.

a = 2.1, b = 7.2,

c = 7.5

Given the three sides lengths choose all options that are true

a)

The sides create an right triangle

b)

The sides create an acute triangle

c)

The sides create an obtuse triangle

d)

The sides do not create a triangle

e)

The sides create an scalene triangle

90.

Which set of side lengths does not form a right triangle?

a)

38, 80, 90

b)

16, 63, 65

c)

36, 77, 85

d)

14, 15, 29

e)

Not enough information to determine if the side lengths form a right triangle.

91.

Jake built a skateboard ramp that covers a horizontal distance of 10 ft. The ramp rises a total of 3.5 ft. What angle does the ramp make with the ground? Round to the nearest degree.

a)

19 degrees

b)

20 degrees

c)

45 degrees

d)

70 degrees

e)

71 degrees

92.

Which of the following is correct for finding the measure of angle Z, choose all that are correct?

a)

∠Z = tan-1 55/48

b)

∠Z = sin-1 48/55

c)

∠Z = cos-1 55/73

d)

∠Z = tan-1 48/73

e)

∠Z = sin-1 48/73

93.

Solve for the missing angle

a)

41.4

b)

0.013

c)

36.9

d)

48.6

e)

53.1

94.

A yacht is anchored 90 feet offshore from the base of a lighthouse. The angle of elevation from the boat to the top of the lighthouse is 26 degrees. The distance between the yacht and the top of the lighthouse is about 100 feet. How far is the boat from the top of the lighthouse??

a)

100 feet

b)

45 feet

c)

110 feet

d)

135 feet

e)

81 feet

95.

Jose would like to know the height of the brick building shown in the picture, if the angle of elevation is 50 degrees and he is 36 feet from the building. Which of these is the calculator ready expression to find the building height?

a)

36 Sin (50)

b)

36 Tan (50)

c)

36 Sin (50) + 6

d)

36 Tan (50) + 6

e)

36 Cos (50) + 6

96.

Henry knows the angle of depression from the lookout and also knows from that angle it is 45 feet in the air. About how far is he from the middle of the lookout tower?

a)

30 feet

b)

45 feet

c)

38 feet

d)

54 feet

e)

59 feet

97.

Susan is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree.

a)

63 ft

b)

65 ft

c)

74 ft

d)

87 ft

e)

125 ft

98.

Solve for the missing distance for the depth of the anchor.

a)

18.9 m

b)

19.5 m

c)

47 m

d)

27.5 m

e)

24.3 m

99.

The pilot of a traffic helicopter sights an accident at an angle of depression of 18 degrees. The helicopter’s altitude is 1560 ft. What is the horizontal distance from the helicopter to the accident? Round to the nearest foot.

a)

507 ft

b)

1640 ft

c)

4801 ft

d)

5048 ft

e)

1884 ft

100.

When the angle of elevation of the sun is 78 degrees, an statue casts a shadow that is 6m long. How far is the top of the statue to the end of its shadow?

a)

5.87 m

b)

28.86 m

c)

28.23 m

d)

1.25 m

e)

13.00 m

101.

Which are equal to the sin30o? Select all that apply.

a)

1/2

b)

0.5

c)

cos 60o

d)

cos 30o

e)

tan 30o

102.

If sin x = cos y, what must be true about x and y?

a)

x + y = 90⁰

b)

x = y

c)

x = 2y

d)

x + y = 180⁰

e)

Not enough information

103.

What is the value of x?

cos (2x - 17) = sin (x - 4)

a)

13

b)

17

c)

21

d)

37

e)

53

104.

cos 40⁰ = ?

a)

sin 50⁰

b)

cos 50⁰

c)

tan 50⁰

d)

sin 40⁰

e)

tan 40⁰

105.

If cosA = sinB then the two angles A and B have to be:

a)

supplementary

b)

Complementary

c)

Adjacent

d)

A linear pair

e)

Parallel

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quiz

Worksheet

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8th - 10th Grade