Free Printable Geometry Final Exam Review

1.

Calculate the angle required to make lines a and b parallel.

(a)

2.

Find the measure of the indicated angle that makes lines u and v parallel.

(a)

3.

Graph the image of the figure using the transformation given: translation 1 unit right.

4.

Graph the image of the figure using the transformation given: reflection across y = -2.

5.

Graph the image of the figure using the transformation given: reflection across y = 1.

6.

Graph the image of the figure using the transformation given: translation 5 units left and 5 units up.

7.

Find the value of x that makes lines u and v parallel.

(a)

8.

Find the value of x that makes lines u and v parallel.

(a)

9.

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

a)

SAS

b)

not congruent

c)

AAS

d)

SSS

10.

Find the distance between each pair of points: (8, 1), (7, 2).

11.

Determine is the two triangles are congruent. If they are, state how you know.

a)

The two triangles are congruent by SSS

b)

The triangles are not congruent.

c)

The triangles are congruent by AAS

d)

The triangles are congruent by SAS

12.

Find the perimeter of the shape ST.

(a)

13.

State if the triangles in each pair are similar. If so, state how you know they are similar and complete the similarity statement.

a)

Yes, the triangles are similar by AA.

b)

Yes, the triangles are similar by SAS.

c)

Yes, the triangles are similar by SSS.

d)

No, the triangles are not similar.

14.

Find the value of each trigonometric ratio:

a)

cos A =

1.

$\frac{3}{5}$

b)

sin A =

2.

$\frac{4}{5}$

c)

tan A =

3.

$\frac{4}{3}$

d)

tan B =

4.

$\frac{3}{4}$

15.

Find the value of each trigonometric ratio:

a)

cos X =

1.

$\frac{12}{13}$

b)

cos Y =

2.

$\frac{5}{13}$

c)

tan Y =

3.

$\frac{12}{5}$

d)

tan X =

4.

$\frac{5}{12}$

16.

Find the missing length indicated.

17.

Solve for x. Each figure is a trapezoid.

18.

Solve for x. Assume that lines which appear tangent are tangent.

19.

Solve for x. Assume that lines which appear tangent are tangent.

20.

Find the measure of the arc or angle indicated.

21.

Find the measure of the arc or angle indicated.

22.

Find the measure of each angle indicated. T

23.

Find the measure of each angle indicated.

24.

Given $m∠KLV$ = 77 degrees and $m∠KLM$ = 173 degrees, find $m∠VLM$ .

25.

Line BC is parallel to Line (a)

Choose from the below words

AD

AB

DC

AC

BD

26.

The transformation that takes the blue image to the red one is (a) over the WX side, then a (b) up.

Choose from the below words

reflection

translation

rotation

transformation

27.

Match the corresponding sides.

a)

MN

1.

s

b)

NO

2.

t

c)

OP

3.

u

d)

PM

4.

r

28.

Triangle GHI is rotated 90 degrees colock-wise and then reflected across the y axis to form Triangle xyz. Match the sides that are equal in length to each other.

a)

GI

1.

y

b)

IH

2.

z

c)

GH

3.

x

29.

Triangle DEF is translated down 9 units and then reflected across the y axis to form Triangle xyz. Match the sides that are equal in length to each other.

a)

DE

1.

y

b)

DF

2.

z

c)

EF

3.

x

30.

Match the following

a)

1.

Reflection over the y-axis

b)

2.

Reflection over the x-axis.

c)

3.

translation

31.

A reflection (a) a figure over a line of reflection in order to create a mirror image.

Choose from the below words

flips

moves

spins

rotates

dilates

32.

Match the following transformations with their rule.

a)

Translated

2 units UP

1.

( x , y + 2)

b)

Translated

2 units DOWN

2.

( x , y - 2 )

c)

Translated

2 units Left

3.

( x - 2 , y )

d)

Translated

2 units Right

4.

( x + 2 , y )

33.

Reflect the given point (-4, 2) over the x-axis and then translate two units to the left.

34.

Match the following transformations with their graphs

a)

1.

Reflection in the x-axis

b)

2.

Reflection in the y-axis

c)

3.

reflection in the line y=x

d)

4.

A translation

e)

5.

A rotation

35.

(a) are the only transformation where the x and y coordinates switch places.

Choose from the below words

Rotations

Reflections

Translations

Dilations

36.

Match the following word with the transformation action:

a)

Translation

1.

Slide

b)

Reflection

2.

Mirror

c)

Rotation

3.

Turn

d)

Dilation

4.

Resize

37.

Plot A' after a translating Point A (2, 6) using the rule:

(x, y) ---> (x - 3, y + 2).

38.

Triangle RST is translated 5 units right and 3 units down. Write a rule that describes this transformation. (x, y) → ( (a) _, (b) _)

Choose from the below words

x+5

y-3

x-3

x-5

-3y

5x

y+3

y+5

39.

Reflect the given point ( -2,-5) over the y-axis and then translate up 3.

40.

Match the following

a)

1.

Reflection over the y-axis

b)

2.

Reflection over the x-axis.

c)

3.

translation

41.

Match the terms with their definitions.

a)

Translation

1.

A transformation that slides a figure.

b)

Rotation

2.

A transformation that turns a figure around a point.

c)

Reflection

3.

A transformation that flips a figure across a line.

42.

JO is the same as (a) , UV is the same as (b) , Angle Y is the same as (c) , and Angle U is the same as (d) .

Choose from the below words

LU

OY

Angle V

Angle O

Angle L

Angle J

LV

JY

43.

∠A =

(a)

Choose from the below words

∠M

∠N

∠L

44.

Angle A is congruent to (a) , and Angle V is congruent to (b) .

Choose from the below words

Angle U

Angle R

Angle S

Angle C

45.

Use the given information to prove that triangles ABC and CDB are congruent. Explain your reasoning.

Triangles ABD and DCB are right triangles (a) AB, BC CD and DA (b) AB=AB (c) . So, triangle ABD and CDB are congruent by (d)

Choose from the below words

because ABCD is a square

are congruent because ABCD is a square

because reflexive property

HL

AAA

Opposite angles are congruent

46.

To solve for x, you should make an equation using (a) . When you solve that, you get x = (b) . When you plug that back in, you can find AM= (c) and since BT is the same as (d) , BT= (e) .

Choose from the below words

AB and AM

4

29

35

MN

AM and MN

1

5

2

13

47.

Remember order matters. Which of the following is true?

(a)

Choose from the below words

∆FGH ≅ ∆VWH

∆FGH ≅ ∆VHW

∆HFG ≅ ∆HWV

∆HGF ≅ ∆VHW

48.

Label the blank triangle with the corresponding triangle part.

a)

|||

b)

|

c)

||

d)

)))

e)

))

f)

)

1

2

3

4

5

6

1)

2)

3)

4)

5)

6)

49.

Given the information in the image, you can deduce that the triangles are (a) because (b)

Choose from the below words

of the ASA Triangle congruence postulate.

of the SSA Triangle congruence theorem.

of the SSS Triangle congruence postulate.

of the HL Triangle congruence postulate.

of the AAS Triangle congruence theorem.

of the SAS Triangle congruence theorem.

there is not enough information given.

congruent

not congruent

50.

Use the congruence statement to answer the following: Angle BAT is (a) , Angle B is (b) , Angle N is (c) ... AT is the same as (d) , and AB is the same as (e) .

Choose from the below words

85 degrees

71 degrees

24 degrees

AN

AM

BT

5 degrees

MN

51.

Given the distance formula is

$\sqrt[]{\left(x-x\right)^2+\left(y-y\right)^2}$

What is the distance between (1,-6),(-5,-2), to the nearest tenth?

52.

Find the distance between the two points. Round to the nearest tenth (one decimal point).

$\left(9,-6\right)$ and $\left(4,\ 5\right)$

53.

Find the distance between each pair of points. Round to the nearest tenth, if necessary.

M(1, 1), N(-10, -10)

54.

Find the distance between each pair of points. Round to the nearest tenth, if necessary.

R(-4, -8), S(2, -3)

55.

Find the distance between each pair of points. Round to the nearest tenth, if necessary.

E(-3, 4), F(-2, 1)

56.

What is the value of "x" in the diagram below?

57.

What is the value of "y" in the diagram below?

a)

2.5

b)

5

c)

5√3

d)

10

58.

Determine the value of: sin(C)

a)

7 / 25

b)

24 / 25

c)

25 / 7

d)

24 / 7

59.

Determine the value of: cos(C)

a)

7 / 25

b)

24 / 25

c)

25 / 7

d)

24 / 7

60.

Determine the value of: tan(C)

a)

7 / 25

b)

24 / 25

c)

25 / 7

d)

24 / 7

61.

Consider angle B in the diagram below.

What is the length of "opposite side" to angle B?

a)

6

b)

8

c)

10

d)

not possible to determine

62.

Match the following side lengths with the correct description of their relationship to angle $\angle B$ in a right triangle.

a)

10

1.

Length of the hypotenuse

b)

8

2.

Length of the adjacent side to $\angle B$

c)

6

3.

Length of the opposite side to angle $\angle B$

63.

How would you find "x" in the diagram?

a)

Multiply 15 by 2.

b)

Divide 15 by 2.

c)

Multiply 15 by √3.

d)

Divide 15 by √3.

64.

Match the following inverse trig functions with the correct scenarios where they would be used to find the measure of an angle.

a)

inverse sine

1.

Scenario where the ratio of the opposite side to the hypotenuse is known.

b)

inverse cosine

2.

Scenario where the ratio of the adjacent side to the hypotenuse is known.

c)

inverse tangent

3.

Scenario where the ratio of the opposite side to the adjacent side is known.

65.

True or False. To find the missing side length in the diagram, use the Pythagorean Theorem.

a)

True

b)

False

66.

Which expression is correct for "y"?

a)

y = tan^–1(31/23)

b)

y = sin^–1(31/23)

c)

y = cos^–1(31/23)

67.

To find "x" in this Special Right Triangle, you would (a) .

Choose from the below words

Divide 10 by 2.

Multiply 10 by 2.

Divide 10 by √3

Multiply 10 by √3

68.

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

a)

Any triangle ever

b)

Non-right triangles only

c)

Right Triangles only

d)

Never

69.

What is the length of side x?

a)

6.57 cm

b)

7 cm

c)

7.44 cm

d)

26.33 cm

70.

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

Choose from the below words

63 ft

65 ft

74 ft

87 ft

71.

Solve for x

a)

9.23

b)

24.36

c)

11.82

d)

19.19

72.

Find the measure of the missing angle.

a)

49^o

b)

50^o

c)

41^o

d)

33^o

73.

Solve for the missing angle

a)

50.2

b)

93.1

c)

12.6

d)

42.2

74.

Find the length of side w.

a)

21.4 cm

b)

18.0 cm

c)

36.5 cm

d)

43.6 cm

75.

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

a)

25 feet

b)

26 feet

c)

27 feet

d)

28 feet

76.

If two lines are perpendicular, they form a ____ degree angle.

77.

Find the length of the missing segment.

a)

12

b)

34

c)

169

d)

13

78.

How can we solve for x in this example?

a)

add both expressions together and subtract from 360

b)

set both expressions equal to each other

c)

use Pythagorean Theorem

d)

use magic

e)

combine like terms

79.

#1 Line AB is tangent to circle C. Find the value of x.

a)

98.18

b)

117

c)

153.3

d)

108

80.

#2 Find the value of x.

(a)

81.

#3 Find the value of x.

a)

4.94

b)

6.94

c)

8.94

d)

2.94

82.

Find the area of a rectangle with length (x - 5) and width (3x + 1).

a)

3x²+16x-5

b)

3x²-14x+5

c)

3x²-14x-5

83.

What is the perimeter of the backyard?

a)

$2x^2+2x-2$

b)

$x^2+x+2$

c)

$3x^2+5x-12$

d)

$x^2-x$

84.

Subtract the following polynomials:

(-5x²+ x³ - 2x + 3) - (-5x² -x³+ 4x + 8)

a)

2x³ - 6x + 11

b)

2x³ - 6x - 5

c)

2x³ - 10x²- 6x - 5

d)

- 10x²- 6x - 5

85.

^{The perimeter of the
triangle is 10x+20. Find the length of the missing side}

a)

6x+10

b)

15x+30

c)

5x+10

d)

5x-10

86.

A translation has occurred, the green shape is the new image label it properly.

a)

A'

b)

B'

c)

C'

d)

D'

1

2

3

4

1)

2)

3)

4)

87.

Plot where y' will be after the transformation.

88.

What is the length of PR?

a)

11

b)

8

c)

5

d)

3

89.

Solve for x.

a)

5

b)

7

c)

14

d)

21

90.

Match the following equations with their correct forms.

a)

2x +20 + 9 = x+21

1.

2x + 29 = x + 21

b)

x + 21 - 9 = 2x + 20

2.

x + 12 = 2x + 20

c)

x+21 - (2x +20) = 9

3.

-x + 1 = 9

91.

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

a)

(5, -2)

b)

(10, -6)

c)

(5, -3)

d)

(2, -2)

92.

The midpoint of the segment with the endpoints: (6, 7) and (6, -5) is (a) .

Choose from the below words

(0, -1)

(6, 1)

(1, 6)

(0, 1)

93.

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

a)

(5,-2)

b)

(5,-3)

c)

(10,-6)

d)

(2,-2)

94.

What is the y-coordinate of the midpoint between (-4,4) and (-2,2)?

a)

3

b)

-3

c)

4

d)

6

95.

What is the x-coordinate of the midpoint between (-4,4) and (-2,2)?

a)

3

b)

-3

c)

4

d)

6

96.

Using R as the reference angle, what is the length of the opposite side?

97.

Using R as the reference angle, what is the length of the adjacent side?

a)

15

b)

17

c)

8

d)

Potato

98.

Using R as the reference angle, what is the length of the hypotenuse?

a)

15

b)

17

c)

8

d)

Potato

99.

Solve for x.

a)

38.9

b)

40.2

c)

45.6

d)

54

100.

The Pythagorean Theorem is (a) (b) (c) (d) (e)

Choose from the below words

$a^2$

$+$

$b^2$

$=$

$c^2$

$x^2$

$-$

$\times$

$\div$

101.

What does SSS stand for?

a)

Small Small Small

b)

Side Side Side

c)

Small Side Small

d)

Sam's Silly Side

102.

State if the two triangles are congruent. If they are, state which theorem you would use.

a)

Yes, SAS

b)

Yes, SSS

c)

Yes, HL

d)

No

103.

Name the postulate, if possible, that makes the triangles congruent.

a)

SAS

b)

ASA

c)

AAS

d)

Not Possible

104.

Name the postulate, if possible, that makes the triangles congruent.

a)

SSS

b)

SAS

c)

ASA

d)

Not Possible

Geometry Final Exam Review

Total questions: 104

Worksheet time: 4hrs 45mins

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