Free Printable Final Review: Geometry

1.

Find the missing side using proportions.

a)

a

b)

b

c)

c

d)

d

2.

Name the corresponding angle or side.

a)

A

b)

B

c)

C

d)

D

3.

a)

A

b)

B

c)

C

d)

D

4.

a)

A

b)

B

c)

C

d)

D

5.

a)

A

b)

B

c)

C

d)

D

6.

a)

A

b)

B

c)

C

d)

D

7.

Which postulate can we use to prove the two triangles are congruent?

a)

SSS

b)

SAS

c)

ASA

d)

AAS

8.

Which postulate can we use to prove the two triangles are congruent?

a)

SSS

b)

SAS

c)

ASA

d)

Not Possible

9.

Which postulate can we use to prove the two triangles are congruent?

a)

SSS

b)

SAS

c)

AAS

d)

Not Possible

10.

Which postulate can we use to prove the two triangles are congruent?

a)

SAS

b)

SSA

c)

ASA

d)

AAS

11.

Congruent by

a)

SSS

b)

SAS

c)

ASA

d)

AAS

12.

$m\angle2=?$

a)

55

b)

125

c)

110

d)

27.5

13.

$m\angle3=?$

a)

55

b)

125

c)

110

d)

27.5

14.

$m\angle1=?$

a)

105.5

b)

101

c)

48

d)

90

15.

GLOT is a kite.
$x=?$

a)

4

b)

2

c)

5.5

d)

3

16.

Kite LMNO is shown.
Solve for x.

a)

90

b)

180

c)

60

d)

75

17.

Kite LMNO is shown.
Solve for x.

a)

32

b)

148

c)

90

d)

58

18.

Find the value of x and y in the kite

a)

x=55 y=35

b)

x=35 y=55

c)

x=145 y=35

d)

x=75 y=35

19.

Find the value of y.

a)

65

b)

110

c)

75

d)

None of these.

20.

The legs of an isosceles trapezoid are _____.

a)

parallel

b)

perpendicular

c)

congruent

d)

skew

21.

Find the midsegment.

a)

14

b)

28

c)

12

d)

16

22.

Find the measure of ∠K:

a)

114°

b)

124°

c)

77°

d)

66°

23.

If ABCD is a parallelogram, what is the length of BD?

a)

10

b)

11

c)

7

d)

5

24.

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

25.

The opposite angles of a parallelogram are ...

a)

complementary

b)

congruent

c)

supplementary

d)

perpendicular

26.

The figure is a parallelogram.
Solve for x.

a)

7

b)

2

c)

0

d)

4

27.

Parallelograms are ...

a)

triangles

b)

quadrilaterals

c)

pentagons

d)

hexagons

28.

A dilation is which of the following:

a)

only an enlargement

b)

only a reduction

c)

Either an enlargement or a reduction

d)

Neither an enlargement or a reduction

29.

A dilation produces a congruent figure

a)

True

b)

False

30.

Similar figures have the same ______ but different ______.

a)

measure; shapes

b)

sizes; shapes

c)

value; measures

d)

shape; sizes

31.

What scale factor was used to produce the image?

a)

2

b)

-2

c)

¹/₂

d)

1

32.

What scale factor was used to produce the image?

a)

2

b)

3

c)

1/3

d)

1/2

33.

Simplify:
√100

a)

1

b)

10

c)

10²

d)

Already simplified

34.

Simplify:
√45

a)

9√5

b)

3√5

c)

5√9

d)

3√15

35.

Simplify:
√200

a)

10√2

b)

2√10

c)

50√2

d)

2√50

36.

a² + b² = c^{2
a = 9 b = 40}

a)

c = 41

b)

c = 65

c)

c = 25

d)

c = 5

37.

Find the length of the missing side.

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

38.

Solve for x. Round to the nearest tenth.

a)

15.3

b)

16.6

c)

24.1

d)

24.3

39.

Solve for x. Round to the nearest tenth.

a)

74.9

b)

3.6

c)

63.5

d)

54.1

40.

Find the value of m.

a)

10

b)

10√2

c)

20√2

d)

√2

41.

Considering the lengths of the sides of the triangle, what measure will < A have to be?

a)

30

b)

45

c)

60

d)

90

42.

What is the exact side length of a square that has a diagonal of 18?

a)

9

b)

18√2

c)

9√2

d)

√2

43.

Find EF.

a)

4

b)

2√2

c)

1

d)

2

44.

Find y.

a)

1

b)

2

c)

2√3

d)

4√3

45.

Which side is the long leg in this 30-60-90 triangle?

a)

4

b)

u

c)

v

46.

What is the measure of side c?

a)

7

b)

7/√2

c)

7√2

d)

14

47.

What type of special triangle is this?

a)

45°-45°-90°

b)

30°-60°-90°

c)

Equiangular

d)

Equilateral

48.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

49.

What is the side of a right triangle across from the right angle called?

a)

square

b)

arm

c)

leg

d)

hypotenuse

50.

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

51.

Do the segment lengths 9, 12, and 15 form a right triangle?

a)

Yes

b)

No

c)

Maybe

d)

Pythagoras

52.

What is the length of y in this 45-45-90 triangle?

a)

8√2

b)

4√2

c)

4

d)

8

53.

Find n.

a)

4

b)

6

c)

12

d)

2√3

54.

BONUS - Solve for x.
You will need to use 45-45-90 and 30-60-90 triangles.

a)

10√3

b)

15

c)

5√3

d)

15√2

55.

The hypotenuse of a right triangle measures 19 meters. One leg measures 15 meters. To the nearest tenth of a meter, what is the length of the other leg?

a)

17.0 meters

b)

24.2 meters

c)

11.7 meters

d)

14.3 meters

56.

What is the formula used to solve for the hypotenuse?

a)

a²⁺b²=c²

b)

a+b=c

c)

a-b=c

d)

c-a=c

57.

An airplane flies 56 miles due north and then 33 miles due east. How many miles is the plane from its starting point?

a)

65 miles

b)

89 miles

c)

45.4 miles

d)

We don't have enough information.

58.

What is the correct ratio you would use to solve for "w"?

a)

sin 40 = w/28

b)

cos 40 = w/28

c)

tan 40 = w/28

d)

sin 40 = 28/w

59.

Which is the correct ratio you would use to solve for "x"?

a)

sin 28 = x/14

b)

cos 28 = x/14

c)

tan 28 = x/14

d)

tan 28 = 14/x

60.

What type of triangles do you use the trig ratios with?

a)

any type

b)

right triangles

c)

obtuse triangles

d)

acute triangles

61.

What is the acronym to help you remember the ratios to use in trigonometry?

a)

RIGHTANG

b)

SOHCAHTOA

c)

SHOCHATOA

d)

SAHCOHTOA

62.

Choose the correct ratio you could use to solve for "x".

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

63.

Find x rounded to the nearest tenth.

a)

46.1

b)

4.9

c)

16.4

d)

26.9

64.

Which trig function would you use to solve this problem for "x"?

a)

Sine

b)

Cosine

c)

Tangent

d)

Pythagorean Theorem

65.

Find the measure of the missing angle to the nearest degree.

a)

49^o

b)

90^o

c)

41^o

d)

33^o

66.

Find the length of side AB.

a)

20 m

b)

5 m

c)

11.54 m

d)

8.66 m

67.

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

a)

49°

b)

57°

c)

45°

d)

54°

68.

Find the value of "x" rounded to the nearest hundredth.

a)

6.09

b)

18.77

c)

5.52

d)

7.68

69.

Are you comfortable with using trig ratios to determine side lengths and angle measures?

Answer honestly. No wrong answer.

a)

I am completely lost. :-(

b)

Off to a good start but could use a little more practice.

c)

So so, but think I am good to go.

d)

I am excelling and want a challenge!

70.

What is the side across from the right angle called?

a)

Leg

b)

Pythagoras

c)

Hypotenuse

d)

Altitude

71.

Which trig function would you use with this diagram?

a)

^Sin

b)

^Cos

c)

^Tan

d)

^Wha??

72.

What is the cosine of angle P?

a)

p/q

b)

q/r

c)

p/r

d)

r/q

73.

Use a calculator to find sin 45.

a)

.707

b)

1

c)

.809

d)

1.4

74.

Use a calculator to find the cos 70.

a)

.12

b)

2.7

c)

.94

d)

.34

75.

Use the calculator to find tan 60

a)

.87

b)

1.7

c)

.5

d)

.11

76.

Use a calculator to find cos 0

a)

4

b)

3

c)

2

d)

1

77.

Use a calculator to find sin 100

a)

.98

b)

.17

c)

-5.6

d)

.76

78.

Find cosA

a)

30/16

b)

30/34

c)

30/15

d)

16/34

79.

What is the ratio for tangent?

a)

O/A

b)

A/O

c)

A/H

d)

O/H

80.

What is the ratio for sine?

a)

O/H

b)

H/A

c)

H/O

d)

O/A

81.

What is the ratio for cosine?

a)

H/A

b)

O/A

c)

A/H

d)

A/O

82.

How do you know which side is the OPPOSITE?

a)

It is next to the right angle

b)

It is opposite the right angle

c)

It is across from the angle

d)

It is the bottom leg of the triangle

83.

If you are given the opposite side and hypotenuse, which trig function should you use?

a)

sine

b)

cosine

c)

tangent

d)

cotangent

84.

Find sinC

a)

21/35

b)

28/21

c)

35/28

d)

28/35

85.

a)

44.55

b)

22.69

c)

41.66

d)

38.49

86.

a)

x = 105.26
y = 98.91

b)

x = 98.91
y = 105.26

c)

x = 47.19
y = 12.31

d)

x = 12.31
y = 47.31

87.

a)

A

b)

B

c)

C

d)

D

88.

What is the correct equation to solve for x ?

a)

tan (58) = x/11

b)

tan (58) = 11/x

c)

cos (58) = x/11

d)

sin (58) = x/11

89.

What is the length of the adjacent side?

a)

8

b)

15

c)

17

90.

Which equation would you use to solve for the unknown angle?

a)

x = sin^–1(4/5)

b)

x = cos^–1(4/5)

c)

x = cos^–1(5/4)

d)

x = tan^–1(4/5)

91.

BONUS - Solve for x.
You will need to use 45-45-90 and 30-60-90 triangles.

a)

10√3

b)

15

c)

5√3

d)

15√2

92.

An airplane flies 56 miles due north and then 33 miles due east. How many miles is the plane from its starting point?

a)

65 miles

b)

89 miles

c)

45.4 miles

d)

We don't have enough information.

93.

What is the acronym to help you remember the ratios to use in trigonometry?

a)

RIGHTANG

b)

SOHCAHTOA

c)

SHOCHATOA

d)

SAHCOHTOA

94.

Choose the correct ratio you could use to solve for "x".

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

95.

Find x rounded to the nearest tenth.

a)

46.1

b)

4.9

c)

16.4

d)

26.9

96.

Find the value of "x" rounded to the nearest hundredth.

a)

6.09

b)

18.77

c)

5.52

d)

7.68

97.

a)

x = 105.26
y = 98.91

b)

x = 98.91
y = 105.26

c)

x = 47.19
y = 12.31

d)

x = 12.31
y = 47.31

98.

What is the length of the adjacent side?

a)

8

b)

15

c)

17

99.

What similarity theorem would prove that these triangles are similar?

a)

SAS∼

b)

SSS∼

c)

AA∼

d)

Side Splitter

100.

Are the triangles similar?

a)

Yes

b)

No

101.

A triangle has sizes measuring 11 cm, 16 cm, and 16 cm. A similar triangle has sides measuring x cm, 24 cm, and 24 cm. What is x?

a)

x = 19 cm

b)

x = 24 cm

c)

x = 3 cm

d)

x = 16.5 cm

102.

What similarity theorem would you use to prove these triangles are similar?

a)

SAS∼

b)

SSS∼

c)

AA∼

d)

BUCK∼

103.

Solve for f.

a)

6

b)

4

c)

3

d)

8

104.

State the postulate that proves these triangles are similar.

a)

SSS

b)

AA

c)

SAS

d)

Not similar

105.

Find side length X.

a)

16

b)

18

c)

2.4

d)

15

106.

Find side length X.

a)

30

b)

25

c)

15

d)

40

107.

Find side length X.

a)

22.5

b)

10

c)

9

d)

7.5

108.

How do these triangles appear to be similar?

a)

AA

b)

SAS

c)

SSS

d)

Not Similar

109.

How do these triangles appear to be similar?
(Hint: Look for non-labeled parts!)

a)

AA

b)

SAS

c)

SSS

d)

Not Similar

110.

How do these triangles appear to be similar?
(Hint: Look for non-labeled parts!)

a)

AA

b)

SAS

c)

SSS

d)

Not Similar

111.

Solve for X.

a)

2 ft

b)

3 ft

c)

4 ft

d)

6 ft

112.

Find x.

a)

54/7

b)

56/3

c)

11

d)

21/2

113.

Mrs. Ashley used similar triangles to make a design. Which statement about the triangles in the design must be true?

a)

They are the same size and shape.

b)

They are the same size but different shapes.

c)

They have corresponding angles that are congruent.

d)

They have corresponding sides that are congruent.

114.

If two figures are similar their angles are______.

a)

proportional

b)

congruent

c)

supplementary

d)

complementary

115.

If two figures are similar, the corresponding sides are ______________.

a)

equal

b)

congruent

c)

proportional

d)

none of these

116.

Are the triangles similar?

a)

Yes

b)

No

117.

Which triangles are similar to triangle A?

a)

B

b)

C

c)

Both

d)

None

118.

Are the following similar? Why or why not?

a)

Yes. All pairs of corresponding angles are congruent.

b)

No, the corresponding angles are not equal.

c)

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

119.

Given that Triangle ABC is similar to Triangle DEF. Find the angle B.

a)

60⁰

b)

42⁰

c)

79⁰

d)

180⁰

120.

Find the value of y.

a)

24

b)

16

c)

6

d)

54

121.

Matching sides are called

a)

Corresponding Sides

b)

Corresponding Angles

c)

The Same

d)

Congruent Sides

122.

What angle corresponds with A?

a)

D

b)

F

c)

C

d)

E

123.

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

a)

4 ft

b)

2 ft

c)

8 ft

d)

6ft

124.

If a 42.9 ft tall statue casts a 253.1 ft long shadow then how long is the shadow that a 6.2 ft tall man casts?

a)

41.7 ft

b)

36.6 ft

c)

34.6 ft

d)

38.8 ft

125.

A power pole 10 m tall casts a shadow 8 meters long, at the same time that a building nearby casts a shadow 14 m long. How tall is the building?

a)

9 m

b)

15.2 m

c)

12 m

d)

17.5 m

126.

A map has a scale of 3 cm:18km. If Oakdale and Woodridge are 54 km apart, then they are how far apart on the map?

a)

15 cm

b)

8.7 cm

c)

9 cm

d)

6 cm

127.

State the postulate that proves these triangles are similar.

a)

SSS

b)

SAS

c)

AA

d)

Not similar

128.

What similarity theorem would you use to prove these triangles are similar?

a)

SAS∼

b)

SSS∼

c)

AA∼

d)

BUCK∼

129.

Find side length X.

a)

30

b)

25

c)

15

d)

40

130.

Find side length X.

a)

22.5

b)

10

c)

9

d)

7.5

Final Review: Geometry

Total questions: 130

Worksheet time: 6hrs 24mins

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