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Geometry Reteach Questions

Total questions: 100

Worksheet time: 2hrs 29mins

Name
Class
Date
1.

What is the probability of spinning green and then a yellow?

a)

0

b)

1/3

c)

4/13

d)

1/36

e)

1/48

2.

A box contains 5 purple marbles, 3 green marbles and 2 orange marbles. Draws are made with replacement.P(both marbles are purple)

a)

2/9

b)

1/3

c)

1/2

d)

1/4

e)

1

3.

P(not A) =

*Remember to simplify.*

a)

1/8

b)

3/4

c)

2/8

d)

1/4

e)

1/3

4.

A jar contains 4 white chips, 5 purple chips, and 1 black chip. Chips are selected randomly one at a time, and are not replaced.

P(white, then purple, then black)

a)

1/36

b)

2/39

c)

5/41

d)

6/43

5.

Victor picks a card at random. Without putting the first card back, he picks a second card at random.

a)

Dependent

b)

Independent

6.

A bag has 3 red marbles, 2 blue and 4 yellow. What is the theoretical probability of pulling a red and then a blue without replacement?

a)

1/12

b)

5/9

c)

2/27

d)

5/18

7.

You flip a nickel three times.

Find the probability that all flips will land on tails.

a)

1/2

b)

1/4

c)

1/6

d)

1/8

8.

Andrew picks one marble at a time from a box and replaces it. He repeats this process 25 times and records the results in the table. Based on the table, what is the likelihood that Andrew drew a green, then a blue, then a yellow, then a red in order?

a)

.3% of the time

b)

3% of the time

c)

30% of the time

d)

100% of the time

9.

Joe decides to roll 2 six sided number cubes and take the sum of both cubes. He wants to know if it is more likely to roll a sum of 7 or a number that is greater than 9. Which of the following is true?

a)

The number seven has the best odds to roll with sum of two sided number cubes so the probability is better than all the numbers greater than 9

b)

There are 3 numbers greater than 9: 10, 11, and 12 so the probability is better to roll one of those 3 numbers

c)

They have the same probability they both have a 6/36 (1/6) chance of happening.

d)

The number cubes are independent events so there is not enough information to decide.

10.
a)

1/48

b)

1/6

c)

1/8

d)

1/24

11.

If a person is chosen at random, what is the probability it is a woman who drives a SUV?

a)

56.25%

b)

75%

c)

83.25%

d)

86.5%

12.

What is the probability of choosing an electrical engineer who likes math?

a)

33.9%

b)

48.6%

c)

16.5%

d)

21.7%

13.

What is the probability out of all those surveyed that they are either a sophomore or eat pizza?

a)

11/50

b)

2/5

c)

13/25

d)

1/10

14.

A survey explored the relationship between gender and band class. Which is a reasonable conclusion?

a)

There are more band members than non-band members

b)

There are more boys in the class than girls

c)

There are more boys in band than not in band

d)

More than half of the bands members in the class are girls

15.

Which is the most likely?

a)

Given that someone buys an SUV, they get it in green.

b)

Given that someone buys a green vehicle, they decide to purchase an SUV.

c)

Someone who buys a vehicle purchases a green SUV.

d)

Someone buys a green vehicle.

16.

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)

17.

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

18.

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

19.

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)

20.

The rule for rotation of 90 degrees counterclockwise is

(x, y) --> _

a)

(y, -x)

b)

(-y, x)

c)

(x, -y)

d)

(-x, y)

e)

(-x,-y)

21.

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)

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)→(-y, -x)

c)

(x, y)→(-x, -y)

d)

(x, y)→(y, -x)

e)

(x, y)→(-y, x)

23.

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

24.

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)

25.

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

26.

Select each answer choice that will map the regular polygon onto itself?

a)

36 degree rotation

b)

90 degree rotation

c)

180 degree rotation

d)

252 degree rotation

e)

270 degree rotation

27.

When performing 2 reflections over parallel lines (as shown in the diagram) what is the resultant transformation?

a)

1 Reflection

b)

1 Rotation

c)

1 Translation

d)

1 Dilation

e)

Not enough information

28.

When performing 2 reflections over non-parallel lines (as shown in the diagram) what is the resultant transformation?

a)

1 Reflection

b)

1 Rotation

c)

1 Translation

d)

1 Dilation

e)

Not enough information

29.

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

30.

Find m∠A.

a)

180

b)

70

c)

54

d)

56

e)

7

31.

In the diagram, which of the following statements are true, choose all that apply?

a)

∠1 and ∠4 are vertical angles

b)

∠4 and ∠5 are alternate interior angles

c)

∠1 and ∠8 are alternate interior angles

d)

∠2 and ∠8 are corresponding angles

e)

∠1 and ∠5 are corresponding angles

32.

Angle 1 = 3x-4

Angle 3 = 5x - 38

Find the measure of Angle 4

a)

17o

b)

47o

c)

133o

d)

55o

e)

163o

33.

Describe the possible lengths for the third side of the triangle given the two sides 10 and 5.

a)

5 < x < 10

b)

0 < x < 10

c)

0 < x < 15

d)

5 < x < 15

e)

5 > x < 10

34.

What is the equation of a line parallel to the following line that passes through the given point?

y = -4x + 6 (2, -1)

a)

y = (1/4)x + 6

b)

y = -4x + 7

c)

y = -4x + 2

d)

y = (1/4)x -1

e)

y= 2x -1

35.

What is the equation of a line that is perpendicular to this line and goes through the given point?

y = 3x + 2 (3, -4)

a)

y = 3x - 2

b)

y = -(1/3)x - 5

c)

y = 3x - 4

d)

y = -(1/3)x - 3

e)

y = -4x +3

36.

What is the equation of the line that passes through point (-2, 6) and is perpendicular to line y=8?

a)

x = -2

b)

y = 6

c)

y = -2x + 6

d)

y = (1/2)x + 6

e)

y = 6x - 2

37.

Order the sides of the triangle from smallest to biggest.

a)

segments DE, EV, DV

b)

segments DV, EV, DE

c)

segments EV, DV, DE

d)

segments DV, DE, EV

e)

Not enough information

38.

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

39.

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

40.

What is the midpoint between (3, -1) and (7, -5)

a)

(5, -2)

b)

(10, -6)

c)

(5, -3)

d)

(2, -2)

e)

(11, -9)

41.

y = 3/2x + 2

y = 2/3x + 6

These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

d)

Not enough information

42.

Choose all the correct statements AB and CD

a)

Parallel

b)

Perpendicular

c)

Neither

d)

Segment AB is congruent to Segment CD

e)

Segment AB is not congruent to Segment CD

43.

Find the endpoint of the segment with the endpoint of (-4, 5) and midpoint of (7, 9)

a)

(18, 13)

b)

(13, 18)

c)

(11,4)

d)

(1.5, -2)

e)

(-15, 1)

44.

Find the y-coordinate of the midpoint of the line

a)

1

b)

2

c)

-2

d)

3

e)

-1

45.

Find the value of x.

a)

74

b)

37

c)

52

d)

105

e)

75

46.

What does it mean if two lines are perpendicular, choose all that apply?

a)

The never intersect

b)

They intersect

c)

The lines form a 90 degree angle

d)

They form a 180 degree angle

e)

The slopes of the lines are the same

47.
a)

-6

b)

-1

c)

1/6

d)

6

e)

-1/6

48.

Which of the following describes AB and CD. Choose all that apply

A(-1,-9), B(5, -6), C(3,2), D(0,8)

a)

parallel

b)

perpendicular

c)

not parallel or perpendicular

d)

congruent

e)

not congruent

49.

Find the slope of the line perpendicular to the given line on the graph.

a)

Undefined

b)

0

c)

1

d)

-1

e)

Infinity

50.

Find the slope of the line parallel to the given line on the graph.

a)

Undefined

b)

0

c)

1

d)

-1

e)

Infinity

51.

An example of coplaner points

a)

D, E, B

b)

C, B, A

c)

M, E, C

d)

A, F, E

e)

D, E, F, Line j

52.

If LM=2x+7, MN=x+9, and LN=40, find the length of segment LM.

a)

8

b)

18

c)

23

d)

17

e)

32

53.

Q is the midpoint of PR.

PQ = 6x – 7 and QR = 5x + 1.

Find the length of PR.

a)

8

b)

16

c)

41

d)

82

e)

29

54.

Find the distance between (-5, -8) and (-1, -16) to the nearest tenth.

a)

8.9

b)

9.8

c)

10.3

d)

11.0

e)

7.8

55.

Find the distance between (-4, 5) and (7, 18) to the nearest hundreth.

a)

15.96

b)

16.0

c)

16.23

d)

17.03

e)

17.0

56.

Choose all of the true statements

a)

M<ABC= 67o

b)

x=43o

c)

x=55o

d)

x=12o

e)

m<ABD=55o

57.

If m<i=40o what is the m< j =

a)

400

b)

45o

c)

50o

d)

90o

e)

140o

58.

1. Find ∠ AOC

a)

130

b)

50

c)

40

d)

55

e)

125

59.

The complement of an angle is five times the measure of the angle itself. Find the angle.

a)

75

b)

15

c)

165

d)

105

e)

not enough information to find the angle

60.

The supplement of an angle is twice as large as the angle itself. Find the complement of the angle.

a)

60

b)

120

c)

30

d)

150

e)

Not enough information to find the complement

61.

Can the plane shown be named plane CBA? Why or why not?

a)

YES because they are all on the same line.

b)

NO because they are all on the same line, which means they form a vertical and horizontal plane.

c)

YES because they are all on the plane.

d)

NO because one of the points is not on the plane.

e)

No planes can only be labeled with one letter plane P

62.
a)

x=3/17

b)

x=9

c)

x=3

d)

x= -3

e)

not enough information to find the value of x

63.

An example of 2 non-collinear points.

a)

D, E

b)

C, B

c)

M, E

d)

F, B

e)

B, E

64.

A plane containing point A.

a)

Plane DEA

b)

Plane k

c)

Plane CDF

d)

Plane j

e)

Plane DEF

65.

A hawk sitting on a tree branch spots a mouse on the ground 15 feet from the base of the tree. The hawk swoops down toward the mouse at an angle of 30 degrees. What is the height of the hawk in the tree?

a)

7.5 ft

b)

15 ft

c)

26 ft

d)

30 ft

e)

15√3 ft

66.

A vertical tower is 20 m high from the horizontal ground. The angle of depression of a ball from the top of the tower is 42°. Calculate the distance, in m, of the ball from the base of the tower

a)

18.01 m

b)

29.89 m

c)

13.38 m

d)

22.21 m

e)

14.86 m

67.

What trigonometric ratio would be used to find the distance from the ship to the plane?

a)

sine

b)

cosine

c)

tangent

d)

inverse cosine

e)

inverse tangen

68.

Solve for the missing angle

a)

41.4

b)

0.013

c)

36.9

d)

48.6

e)

53.1

69.

Which of the following MUST be used to find the measure of an angle in a right triangle given 2 sides?

a)

Pythagorean theorem

b)

Sin, Cos, or Tan

c)

Sin-1, Cos-1, or Tan-1

d)

Chord-Chord Product Theorem

e)

SOHCAHTOA

70.

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

71.

Which sides are given?

a)

Adjacent and Hypotenuse

b)

Opposite and Adjacent

c)

Opposite and Hypotenuse

d)

Hypotenuse only

e)

Not enough information

72.

Which trigonometric function will you use given the sides?

a)

Sine

b)

Cosine

c)

Tangent

d)

SOH CAH TOA

e)

Pythagorean Theorem

73.

Which scenario describes the picture shown?

a)

A 5 foot ramp is 8 feet away from a building. What is the angle that the ramp makes with the ground?

b)

A 5 foot ramp leans against an 8 foot structure. What is the angle that the ramp makes with the ground?

c)

An 8 foot ramp leans

against a building 5 feet away. What angle does the ramp make with the ground?

d)

A 5 foot man is 8 feet away from a building. What is the angle of elevation?

e)

None of these scenarios match the situation in the picture.

74.
a)

27/36

b)

27/45

c)

45/36

d)

45/27

e)

36/27

75.

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)=x/14

76.

Choose the correct ratio.

a)

sinZ=5/13

b)

sinX=5/13

c)

cosX=13/12

d)

tanZ=12/5

e)

tanX=5/12

77.

What is the correct ratio?

a)

3/5

b)

3/4

c)

4/5

d)

4/3

e)

5/3

78.

cos(43) =

a)

sin(43)

b)

sin(47)

c)

1/sin(43)

d)

cos(47)

e)

tan(43)

79.

What is the measure of <A?

a)

xo

b)

(90 - x)o

c)

(x + 90)o

d)

(180 - 2x)o

e)

(180 - 90- 2x)o

80.

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

81.

If you are given the hypotenuse and an adjacent side, which should you use to find the the other side length?

a)

sine

b)

cosine

c)

tangent

d)

cotangent

e)

Pythagorean theorem

82.

Find h

a)

35.60

b)

35.00

c)

35.71

d)

61.03

e)

60

83.

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)

23 miles

84.

Use inverse trig ratios (SOH CAH TOA) to solve for the missing angle

a)

33°

b)

49°

c)

39°

d)

41°

e)

34°

85.

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)

28 degrees

d)

35 degrees

e)

45 degrees

86.

What is the measure of angle 2?

a)

50 degrees

b)

57.5 degrees

c)

65 degrees

d)

115 degrees

e)

180 degrees

87.

Fill in the missing proofs.

a)

Transitive Property, SAS(Side-Angle-Side)

b)

Reflexive Property, SAS(Side-Angle-Side)

c)

Reflexive Property, Vertical Angles Thm.

d)

Transitive Property, SSS(Side-Side-Side)

e)

Vertical Angles AAS(Angle-Angle-Side)

88.

How are these triangles congruent?

a)

AAA

b)

SAS

c)

ASA

d)

HL

e)

Not enough information

89.

What is the measure of angle b?

a)

36o

b)

56o

c)

63o

d)

81o

e)

117o

90.

Find x.

a)

x = 118

b)

x = 31

c)

x = 23

d)

x = 62

e)

Not enough information

91.

The triangles are congruent. Which of the following statements must be true?

a)

∠A ≅ ∠D

b)

∠B ≅ ∠E

c)

AB ≅ DE

d)

BC ≅ FD

e)

∠C ≅ ∠F

92.

∆EHG≅∆KFC

Which is a true statement?

a)

EH≅FK

b)

HG≅KF

c)

EG≅KC

d)

∠E≅∠C

e)

∠G≅∠F

93.

What is the value of x?

a)

20o

b)

60o

c)

15o

d)

40o

e)

8 in.

94.

What is the length of EF?

a)

8

b)

9

c)

16

d)

17

e)

18

95.

Choose all the sets of triangles are congruent

a)
b)
c)
d)
e)
96.

How are these two triangles congruent?

a)

SAS

b)

ASA

c)

AAS

d)

SSA

e)

HL

97.

Choose all the statements that would prove the two triangles congruent

a)

U is the midpoint of segment XV

b)

U is the midpoint of segment YW

c)

Segment XY is congruent to segment WV

d)

Angle X is congruent to angle V

e)

Angle Y is congruent to angle W

98.

How are these two triangles congruent?

a)

SAS

b)

SSA

c)

ASA

d)

AAS

e)

Not enough information

99.

in triangle ABC, Johnny know that AB=BC. The triangle is not equalateral. Johnny states that triangle ABC is isosceles. Therefore, she consludes that angle A and angle B must be congruent to one another.

Is Johnny's conclusion correct? Why or why not?

a)

Johnny's conclusion is correct. In an isosceles triangle, the base angles are always the first two letters in the name of the triangle.

b)

Johnny's conclusion is correct. In an isoceles triangle, all 3 angles are congruent to one another. Therefore angle A and angle B must be congruent to one another.

c)

Johnny's conclusion was incorrect. She cannot state that triangle ABC is isosceles just because AB=BC

d)

Johnny's conclusion was incorrect. If AB=BC, then the base angles of the isosceles triangle would be angle A and angle C, not angle A and angle B

e)

None of these will allow Javier to prove congruence.

100.

Lizbeth wants to prove that the base angles of an isosceles triangle are congruent. To do this, he draws triangle ABC, with AB=BC. He will prove that angle A and angle C are congruent by dividing triangle ABC into two triangles using triangle congruence.

Which of the following must be part of Lizbeth's Proof?

a)

Drawing a line parallel to AC through the Midpoints of AB and BC

b)

Drawing a line parallel to BC through the Midpoints of AB and AC

c)

Drawing a line perpendicular to AC through point B

d)

Drawing a line perpendicular to AC through point B

e)

Not enough information

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