Free Printable Geometry Final Review

1.

Given two points (x₁, y₁), (x₂, y₂) the distance between them is:

a)

b)

c)

d)

2.

Which of the following is the correct midpoint formula given two endpoints (x₁, y₁) and (x₂, y₂)?

a)

b)

c)

d)

3.

What is the distance between the two points?

a)

6.3

b)

6.5

c)

6.7

d)

16

4.

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

a)

8.9

b)

9.8

c)

10.3

d)

11

5.

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

a)

(5, -2)

b)

(10, -6)

c)

(5, -3)

d)

(2, -2)

6.

Find the midpoint of the segment with the endpoints: (-2, 6) and (-3, 7)

a)

(0.5, 0.5)

b)

(6.5, -2.5)

c)

(-1.5, 7)

d)

(-2.5, 6.5)

7.

Find the y-coordinate of the midpoint of the line

a)

1

b)

2

c)

-2

d)

3

8.

Reflect the point (2, -4) over the y-axis.

a)

(-4, 2)

b)

(-2, 4)

c)

(-2, -4)

d)

(2, 4)

9.

What transformation is happening?

T_{(x + 2, y - 3)}

a)

translate up 2, left 3

b)

translate right 2, up 3

c)

translate right 2, down 3

d)

translate left 3, right 2

10.

Reflect (6, -3) over the line x-axis.

a)

(6, 3)

b)

(-6, -3)

c)

(-3, 6)

d)

(3, -6)

11.

Rotate the point (7,8) around the origin 90 counter clockwise degrees. State the image of the point.

a)

(-7,-8)

b)

(8,-7)

c)

(-8,7)

d)

(8,7)

12.

If you were to rotate ABCD 180° about the origin, what would the coordinate of A' be?

a)

(-5, 5)

b)

(-3, -5)

c)

(-5, 3)

d)

(-3, 3)

13.

How many degrees COUNTERCLOCKWISE was quadrilateral ABCD rotated?

a)

90°

b)

180°

c)

270°

d)

360°

14.

Determine how to translate triangle ABC to triangle A'B'C'.

a)

(x-2, y+5)

b)

(x+2, y-9)

c)

(x-2, y+9)

d)

(x-9, y+2)

15.

Where would point J' be if you translated point J 5 units to the left and 2 units up?

a)

(5, 3)

b)

(3, -5)

c)

(-5, 3)

d)

(-3, 5)

16.

Which answer shows a reflection across the y-axis?

a)

a

b)

b

c)

c

d)

d

17.

Reflect the point D (-9, -12) over the line y = -x.

a)

(12, 9)

b)

(-12, -9)

c)

(-12, 9)

d)

(12, -9)

18.

Find the coordinates of E' after a rotation 90^o clockwise.

a)

E' (3, -2)

b)

E' (2, 3)

c)

E' (3, 2)

d)

E' (-3, -2)

19.

In this picture,

a)

<BCA=<DCE because they are vertical angles and vertical angles are always congruent to each other

b)

<C=<C because they are vertical angles and vertical angles are always congruent to each other

c)

<EDC=<ACB because they are vertical angles and vertical angles are always congruent to each other

d)

None of the above; we don't actually have vertical angles

20.

If AD bisects <EDI, then

a)

<ADE=<IDA

b)

IA=AE

c)

ID=ED

d)

All of the above

21.

If L is the midpoint of TJ, what must be true?

a)

TL=JT

b)

JL=TJ

c)

TL=LJ

d)

T is also the midpoint of JL

22.

If DA bisects IE, then

a)

ID=ED

b)

IA=EA

c)

<IDA=<EDA

d)

<IAD and <EAD are right angles

23.

State if the two triangles are congruent. If they are, state how you know.

a)

A

b)

B

c)

C

d)

D

24.

When using hypotenuse leg (HL) in a proof, you must first state ...

a)

CPCTC.

b)

there are right triangles.

c)

that vertical angles are congruent.

d)

the reflexive property.

25.

What is statement #1?

a)

b)

Given

c)

$\angle BCA\cong\angle DCE$

d)

26.

What is the reason for statement #2.

a)

Definition of midpoint

b)

Definition of congruent

c)

Definition of angle bisector

d)

Definition of segment bisector

27.

Identify the missing statement or reason

a)

Reflexive Property

b)

Definition of Midpoint

c)

Given

d)

Vertical Angles Theorem

28.

State if the two triangles are congruent. If they are, state how you know.

a)

A

b)

B

c)

C

d)

D

29.

State if the two triangles are congruent. If they are, state how you know.

a)

A

b)

B

c)

C

d)

D

30.

What additional information is required for the 2 triangles to be congruent by ASA?

a)

A

b)

B

c)

C

d)

D

31.

What additional information is required for the 2 triangles to be congruent by SAS?

a)

A

b)

B

c)

C

d)

D

32.

What does CPCTC stand for?

a)

Corresponding Parts of Corresponding Triangles are Congruent

b)

Congruent Parts of Corresponding Triangles are Congruent

c)

Corresponding Parts of Congruent Triangles are Congruent

33.

The opposite angles of a parallelogram are ...

a)

complementary

b)

congruent

c)

supplementary

d)

perpendicular

34.

In a parallelogram, consecutive angles are __________.

a)

congruent

b)

supplementary

c)

corresponding

d)

parallel

35.

In a parallelogram, diagonals are __________.

a)

perpendicular

b)

bisected

c)

congruent

d)

parallel

36.

Which is NOT a property of a parallelogram?

a)

Diagonals bisect each other

b)

Diagonals are congruent

c)

Both pairs of opposite sides are parallel

d)

Both pairs of opposite angles are congruent

37.

The opposite sides of a parallelogram are congruent.

a)

true

b)

false

c)

maybe

d)

sometimes

38.

Find m∠U.

a)

95°

b)

85°

c)

75°

d)

90°

39.

Find the m∠R.

a)

40°

b)

140°

c)

50°

d)

180°

40.

Find x.

a)

75

b)

85

c)

105

d)

95

41.

Find x.

a)

85

b)

105

c)

95

d)

75

42.

Find x.

a)

82

b)

92

c)

98

d)

102

43.

Find x.

a)

103

b)

77

c)

83

d)

73

44.

Find x.

a)

89

b)

101

c)

81

d)

79

45.

A telephone booth that is 8ft tall casts a shadow that is 4ft long. Find the height of a lawn gnome that casts a 2ft shadow.

a)

2 ft

b)

4 ft

c)

6 ft

d)

8 ft

46.

The triangles are similar. Solve for x.

a)

4

b)

5

c)

6

d)

7

47.

Solve for x.

a)

8

b)

6

c)

5

d)

-8

48.

Solve for x and y.

a)

x=11.43, y=42.78

b)

x=11.43, y=192.5

c)

x=14, y=48

d)

x=10, y=11.43

49.

One property of similar triangles is that corresponding angles of two similar triangles are congruent. What is the second property of similar triangles?

a)

Corresponding sides are congruent

b)

Corresponding sides are unrelated

c)

Corresponding sides are equal

d)

Corresponding sides are equally proportional

50.

What side corresponds with DE?

a)

CA

b)

AB

c)

EC

d)

BA

51.

What side corresponds with BC?

a)

FD

b)

ED

c)

EC

d)

CB

52.

What is the value of X?

a)

1.92

b)

2.04

c)

2.15

d)

2.5

53.

Determine whether the triangles are similar.

a)

SSS~

b)

AA~

c)

SAS~

d)

not similar

54.

Are the following similar? Why or why not?

a)

Yes

b)

No, the corresponding angles are not equal.

c)

No, the ratios of the corresponding sides are not equal.

55.

Tell whether the two figures are similar. Explain your reasoning. (Hint: are they proportional?)

a)

Yes, similar because they are the same shape and side lengths are proportional.

b)

No, not similar because they are the same shape, but side lengths are not proportional.

c)

Yes, same shape

d)

No, different sizes

56.

The measures of two complementary angles are in the ratio 2:3. What is the measure of the smaller angle?

a)

18

b)

36

c)

54

d)

90

57.

The perimeter of a rectangle is 280 cm. The ratio of the width to the length is 3:4. What is the length of the rectangle?

a)

20

b)

40

c)

60

d)

80

58.

The measures of the angles of a triangle are in the extended ratio 4:3:2. What is the measure of the largest angle?

a)

20

b)

40

c)

60

d)

80

59.

What is the saying we use to remember the trig functions?

a)

SOH CAH TOA

b)

SAH COH TAO

c)

COH SAH TOA

d)

SOH COH TOH

60.

$\sin\theta=$

a)

$\frac{opposite}{hypotenuse}$

b)

$\frac{hypotenuse}{opposite}$

c)

$\frac{adjacent}{hypotenuse}$

d)

$\frac{opposite}{adjacent}$

61.

$\cos\theta=$

a)

$\frac{opposite}{hypotenuse}$

b)

$\frac{hypotenuse}{adjacent}$

c)

$\frac{adjacent}{hypotenuse}$

d)

$\frac{opposite}{adjacent}$

62.

$\tan\theta=$

a)

$\frac{opposite}{hypotenuse}$

b)

$\frac{hypotenuse}{adjacent}$

c)

$\frac{adjacent}{opposite}$

d)

$\frac{opposite}{adjacent}$

63.

Find the length of side W?
sin 68 = 70/w

a)

186.86 m

b)

75.50 m

c)

28.28 m

d)

.01 m

64.

Solve for x. Round to the nearest tenth.

a)

7.5

b)

34.1

c)

14.1

65.

a)

18.9

b)

19.5

c)

47

d)

27.5

66.

What is the length of side x?

a)

6.57 cm

b)

7 cm

c)

7.44 cm

d)

26.33 cm

67.

Find h₁

a)

6.69 ft

b)

11.11 ft

c)

9.00 ft

d)

7.43 ft

68.

Find h₂

a)

16.73 ft

b)

22.51 ft

c)

18.59 ft

d)

20.79 ft

69.

Find the measure of the missing angle.

a)

64^o

b)

26^o

c)

61^o

d)

.008^o

70.

Solve for the missing angle

a)

50

b)

0.053

c)

36.9

d)

95

71.

Solve for the missing angle.

a)

45^o

b)

90^o

c)

22.5^o

d)

128^o

72.

What is the measure of arc AB? (Note: BD is a diameter)

a)

140

b)

142

c)

180

d)

153

73.

Find the measure of arc JH. (Hint: JG is a diameter)

a)

93

b)

130

c)

120

d)

95

74.

What is the measure of ∠PTQ?

(Remember there is a total of 360º in a circle)

a)

100°

b)

140°

c)

180°

d)

120°

75.

What is the measure of arc QRS? (Note: QS is a diameter)

a)

360

b)

180

c)

90

d)

64

76.

Find the measure of arc AB.

a)

17

b)

34

c)

68

d)

146

77.

What is the measure of arc KL?

a)

108

b)

106

c)

110

d)

112

78.

What is the measure of angle DEF?

a)

72

b)

73

c)

74

d)

75

79.

a)

A

b)

B

c)

C

d)

D

80.

Find $m\angle\ B$ (Hint: first find arc BD to get arc CD)

a)

A

b)

B

c)

C

d)

D

81.

Write the equation of a circle with center (7, 0) with radius 3.

a)

(x - 7)² + y² = 9

b)

x² + (y -7)² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

82.

What are the coordinates of the center and the radius of the circle with equation:

(x - 4)² + (y - 3)² = 25 ?

a)

Center (4,3)

Radius = 5 units

b)

Center (4,3)

Radius = 25 units

c)

Center (-4,-3)

Radius = 25 units

d)

Center (-4,-3)

Radius = 5 units

83.

See Picture

a)

A

b)

B

c)

C

d)

D

84.

The diameter of a circle has length 12. The center is at (-5, 2). Give the equation of the circle.

a)

(x - 2)²+ (y + 5)²= 36

b)

(x - 5)² + (y + 2)² = 6

c)

(x + 5)²+ (y - 2)²= 36

d)

(x + 2)²+ (y - 5)²= 6

85.

The point (-5,6) is on a circle with center (-1,3). Write the equation of the circle.

a)

(x+5)²+(y-6)²=25

b)

(x-5)²+(y-2)²=25

c)

(x+1)²+(y-3)²=25

d)

(x-1)²+(y+3)²=25

86.

A ___________ polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

a)

plain

b)

perfect

c)

regular

d)

magical

87.

What does the 'a' stand for in the following formula?

a)

area

b)

apossum

c)

altitude

d)

apothem

88.

What would be the first step in finding the area of the pentagon?

a)

draw in the apothem

b)

calculate the length of the side

c)

calculate the length of the radius

d)

find the angle measure

89.

Find the area of this composite figure

a)

71 cm²

b)

72 cm²

c)

73 cm²

d)

74 cm²

90.

find the area

a)

19.5

b)

78

c)

39

d)

27

91.

Which is the apothem?

a)

AD

b)

AB

c)

CD

d)

CB

92.

What is the surface area of this figure?

a)

200 cm ²

b)

800 cm ²

c)

400 cm ²

d)

1500 cm ²

93.

A rectangular brick has a length of 5 centimeters, a width of 9 centimeters and a surface area of 650 cm². What is the height of the brick?

a)

20 cm

b)

43 cm

c)

14 cm

d)

10 cm

94.

Given a cylinder with a surface area of 2543 cm²and radius of 9 cm, calculate the height of this cylinder to the nearest tenth.

a)

36.0 cm

b)

45.0 cm

c)

10 cm

d)

282.6 cm

95.

Campbell Soup is creating a new soup label. If a can has a height of 6 in and a diameter of 4 in, how much material does Campbell need for each soup label?

a)

75.40 in²

b)

75.40 in

c)

175.93 in

d)

175.93 in²

96.

Calculate the surface area.

a)

904.78 mm²

b)

452.39 mm²

c)

3,216.99 mm²

d)

3,392.92 mm²

97.

A party hat has a diameter of 18 centimeters and a slant height of 7 centimeters. Calculate the amount of material it takes to make this party hat.

a)

904.8 cm²

b)

395.8 cm²

c)

254.5 cm²

d)

452.4 cm²

98.

Find the volume of the figure.

a)

1,800 cm³

b)

900 cm³

c)

600 cm³

d)

750 cm³

Geometry Final Review

Total questions: 98

Worksheet time: 5hrs 32mins

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