Free Printable Geometry Final Exam Review 2026

1.

Find the length of the missing side.

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

2.

When do we use the Pythagorean Theorem?

a)

To find a missing angle in a right triangle

b)

To find the missing length of a right triangle

c)

To find the area of a right triangle

3.

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

a)

Yes

b)

No

c)

Maybe

d)

Pythagoras

4.

Would a triangle with these side lengths be a right triangle?
4, 5, 6

a)

Yes

b)

No

5.

Solve for x. SIMPLIFY your radical answer completely.

a)

4√22

b)

22√4

c)

22√2

d)

2√22

6.

Classify the triangle with the given lengths: 8,15,17

a)

Acute

b)

Right

c)

Obtuse

d)

Not a Triangle

7.

Classify the triangle with the given lengths: 2, 3, 5

a)

Acute

b)

Right

c)

Obtuse

d)

Not a Triangle

8.

Classify the triangle with the given lengths: 8,9,15

a)

Acute

b)

Right

c)

Obtuse

d)

Not a Triangle

9.

Use the Pythagorean Theorem to find x, the length of the diagonal.

a)

50

b)

75

c)

64

d)

45

10.

^{Find the length of the missing side}

a)

48

b)

108

c)

83.6

d)

72

11.

Find the length of the missing side.

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

12.

^{Find the missing side}

a)

11

b)

61

c)

$\sqrt{61}$

d)

$\sqrt{11}$

13.

Which is a Pythagorean Triple?

a)

4,5,12

b)

8,15,17

c)

7,21,28

d)

9,27,36

14.

Which is a Pythagorean Triple?

a)

7,24,25

b)

3,6,9

c)

10,11,13

d)

2,4,6

15.

Which is a Pythagorean Triple?

a)

2,8,12

b)

9,40,41

c)

24,25,29

d)

6,11,14

16.

Given a triangle with sides a, b, and c:

if $c^2<a^2+b^2,$ then the triangle is ______.

a)

acute

b)

obtuse

c)

right

17.

Given a triangle with sides a, b, and c:

if $c^2>a^2+b^2,$ then the triangle is ______.

a)

acute

b)

obtuse

c)

right

18.

If the given side lengths form a triangle, then classify the triangle as acute, right, or obtuse.

9, 14, 16

a)

Acute

b)

Right

c)

Obtuse

19.

Find the altitude in the following isosceles trapezoid.

a)

√72

b)

6√2

c)

3

d)

9

20.

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

a)

4

b)

u

c)

v

21.

I have been given the short leg in this 30-60-90 triangle. How do I find the long leg?

a)

Multiply 4 by 2

b)

Multiply 4 by √3

c)

Multiply 4 by √2

d)

Divide 4 by 2

22.

What are x and y in this 30-60-90 triangle?

a)

x = 6 y = 3√3

b)

x = 3√2 y = 3

c)

x = 3√3 y = 6

d)

x = 6 y = 3√2

23.

Find the value of x.

a)

18

b)

18√3

c)

36√3

d)

12

24.

In this 45-45-90 triangle, I have been given a leg, so to find the other leg I...

a)

Multiply that leg by 2

b)

Use the same length for the second leg

c)

Multiply that leg by √2

d)

Divide that leg by √2

25.

Find x - the length of the hypotenuse of the triangle.

a)

5

b)

5√2

c)

10

d)

5√3

26.

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

a)

8√2

b)

4√2

c)

4

d)

8

27.

What are a and b in this 30-60-90 triangle?

a)

b=3.5√3 a = 7√3

b)

b = 7 a = 7√2

c)

b = 7 a = 14

d)

b = 7√3 a = 14√3

28.

What are x and y in this 30-60-90 triangle?

a)

x = 6 y = 3√3

b)

x = 1.5√3 y =1.5

c)

x = 3√3 y = 6

d)

x = √3 y = 2√3

29.

What are u and v in this 30-60-90 triangle?

a)

v = 2√3 u = 6

b)

v = 4 u = 4√3

c)

v = 4 u = 4√2

d)

v = 4√3 u = 8√3

30.

Find the length of m.

a)

4

b)

6

c)

12

d)

2√3

31.

Divide $\frac{4}{\sqrt{3}}$

a)

$\frac{4\sqrt{3}}{3}$

b)

$\frac{4\sqrt{3}}{2}$

c)

$4\sqrt{3}$

32.

Determine the value of c.

a)

$c=6\ \sqrt[]{3}$

b)

$c=12\ \sqrt[]{3}$

c)

$c=18$

d)

$c=36$

33.

Find b.

a)

$10\ \sqrt[]{2}$

b)

$20\ \sqrt[]{2}$

c)

$20$

d)

$40$

34.

Determine the value of x.

a)

$x=10\ \sqrt[]{2}$

b)

$x=10$

c)

$x=5\ \sqrt[]{3}$

d)

$x=5\ \sqrt[]{6}$

35.

A square has a diagonal of length $14\ \sqrt[]{3}$ . What is the length of each side?

a)

$7\ \sqrt[]{6}$

b)

$7\ \sqrt[]{3}$

c)

$14\ \sqrt[]{6}$

d)

$14$

36.

What equation can be used to solve for x?

a)

Sin(40°)= x/40

b)

Sin(40º)=x/19

c)

Cos(40º)=x/19

d)

Tan(40°)=19/x

37.

Solve for x. Round to the nearest tenth.

a)

9.8

b)

0.1

c)

0.038

d)

9.9

38.

Choose the correct ratio.

a)

cos(33^o)=x/14

b)

sin(33^o)=x/14

c)

cos(33^o)=14/x

d)

sin(33^o)=14/x

39.

Which trigonometric ratio is correct?

a)

sinA= opp/adj

b)

cosA= opp/hyp

c)

tanA= opp/adj

d)

sinA= adj/opp

40.

Choose the correct ratio.

a)

sinZ=5/13

b)

sinX=5/13

c)

cosX=13/12

d)

tanZ=12/5

41.

Which one is the easy way to remember trigonometric ratios?

a)

Sah Coh Toa

b)

Soh Cah Toa

c)

Soh Cah Tao

d)

Soh Ceh Toa

42.

What is the value of x?

a)

9.17

b)

98.13

c)

0.11

d)

26.69

43.

What is the value of x?

a)

17.30

b)

11.33

c)

0.06

d)

23.82

44.

Find the measure of the indicated angle.

a)

$6^{\circ}$

b)

$20^{\circ}$

c)

$43^{\circ}$

d)

$47^{\circ}$

45.

Solve for x. Round to the nearest tenth.

a)

103.5

b)

4.7

c)

55.0

d)

23.4

46.

Set up the problem...

a)

sin X = 41/28

b)

tan X = 41/28

c)

cos X = 28/41

d)

sin X = 28/41

47.

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

48.

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

a)

32°

b)

44°

c)

61°

d)

50°

49.

Find the measure of the missing angle.

a)

49^o

b)

50^o

c)

41^o

d)

33^o

50.

If you are given the two sides that are not the hypotenuse, which trig function should you use?

a)

sine

b)

cosine

c)

tangent

d)

cotangent

51.

Set up the equation to solve for the marked angle.

a)

$\theta\ =\tan^{-1}\left(\frac{14}{29}\right)$

b)

$\tan\ \theta=\frac{14}{29}$

c)

$\theta=\tan^{-1}\left(\frac{29}{14}\right)$

d)

$\theta\ =\tan\ \left(\frac{29}{14}\right)$

52.

Sam views a deer from a height of 45 feet. The horizontal distance between the tourist and the deer is 130 feet. At what angle (x) should the tourist hold his camera to photograph the deer? Round your answer to the nearest degree.

a)

19^o

b)

45^o

c)

71^o

d)

138^o

53.

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

a)

111.8 yards

b)

115 yards

c)

127.3 yards

d)

119 yards

54.

Kevin leans a 16 foot ladder l against a building. If the angle the ladder makes with the ground is 68°, how high up the building does the ladder reach?

a)

39.6

b)

6.0

c)

14.8

d)

13.6

55.

Jordan is stuck at the top of a Ferris wheel. Her mother is standing 38 feet from the base of the wheel watching her. If the angle of elevation from Jordan's mom to Jordan is 73^o, how far off the ground is Jordan?

a)

118.2 ft

b)

120.9 ft

c)

124.3 ft

d)

126.5 ft

56.

Jovanni's height is 2 m. The distance between Jovanni and the flag pole is 10 m. The angle of elevation from Jovanni to the top of the flagpole is 56°. How tall is the flagpole?

a)

14.83

b)

16.83

c)

18.83

d)

20.83

57.

Which of the following formulas shows the Law of Cosines?

a)

c² = a² + b² - 4ac + cosA

b)

c² = a² - b² - 2abcosC

c)

c² = a² + b² - 2abcosC

d)

(cos A)/a = (cos B)/b

58.

Identify the Law of Sines

a)

Sin²x + Cos²x =1

b)

Sin(A)/a = Sin(B)/b = Sin(C)/c

c)

Sin(A)Sin(B)Sin(C) = 1

d)

y=Sin(x)

59.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

60.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

61.

What is the measure of angle A?

a)

50 degrees

b)

60 degrees

c)

78 degrees

d)

74 degrees

62.

Find AC

a)

12

b)

10

c)

23

d)

14

63.

Calculate the length of AC

a)

30

b)

24

c)

27

d)

35

64.

Calculate the length of BC

a)

24

b)

20

c)

27

d)

23

65.

Which law would you use?

a)

Law of Sines

b)

Law of Cosines

66.

Which law would you use?

a)

Law of Sines

b)

Law of Cosines

67.

What is the correct set up to find side p?

a)

$p^2=16^2+19^2-2\left(16\right)\left(19\right)\cos48$

b)

$p^2=16^2-19^2+2\left(16\right)\left(19\right)\sin48$

c)

$p^{ }=16^{ }+19^{ }+2\left(16\right)\left(19\right)\cos48$

d)

$16^2=p^2+19^2-5\left(16\right)\left(19\right)\cos48$

68.

8.Solve for x

a)

3.85

b)

4.25

c)

3.35

d)

5.65

69.

Find a

a)

54

b)

45

c)

40

d)

51

70.

Find a

a)

6

b)

23

c)

5

d)

17

71.

Find c

a)

35

b)

45

c)

41

d)

37

72.

What part of the circle is present?

a)

diameter

b)

radius

c)

chord

d)

secant

73.

The distance from the center of a circle to a point on the circle. Endpoints are the center and a point on the circle.

a)

Radius

b)

Circumference

c)

Diameter

d)

Segment Length

74.

Distance across a circle, through the center of the circle.

a)

Diameter

b)

Radius

c)

Chord

d)

Segment

75.

A segment whose endpoints are points on the circle.

a)

Chord

b)

Tangent

c)

Secant

d)

Angle

76.

A segment that touches a circle at exactly one point.

a)

Tangent

b)

Segment

c)

Secant

d)

Chord

77.

The distance around the circle (perimeter)

a)

Circumference

b)

Area

c)

Circle

d)

Length

78.

An arc that measures between 180 and 360 degrees.

a)

Major Arc

b)

Minor Arc

c)

Arc

d)

Semicircle

79.

An angle whose vertex lies of the circle and both endpoints lie across the circle.

a)

Inscribed Angle

b)

Central Angle

c)

Angle

d)

Arc

80.

Line LQ

a)

Secant

b)

Tangent

c)

Chord

d)

Diameter

81.

Angle NQR

a)

Inscribed Angle

b)

Central Angel

c)

Triangle

d)

Secant

82.

Segment QR

a)

Chord

b)

Secant

c)

Diameter

d)

Radius

83.

Name a secant.

a)

BD

b)

DG

c)

HF

d)

AF

84.

Name a radius.

a)

AF

b)

CD

c)

HJ

d)

DG

85.

Name a tangent.

a)

BD

b)

AF

c)

BJ

d)

HF

86.

A hula hoop has a diameter of 3 feet. What is it's area?

a)

18.85 ft²

b)

9.42 ft²

c)

28.26 ft²

d)

7.07 ft²

87.

A DVD has a diameter of 15 millimeters. Which equation would help you determine the circumference?

a)

c = 15π

b)

C = 2π15

c)

c = 15 ÷ π

d)

c = 15 π

88.

Other than the formula C=πd what is another formula for circumference of a circle?

a)

C=2π

b)

C=2πr

c)

C=πr²

d)

C=πd²

89.

Find the length of the arc. Leave answer in terms of pi.

a)

$6\pi$ inches

b)

$27\pi$ inches

c)

$18\pi$ inches

d)

$12\pi$ inches

90.

If r = 8 cm, find the EXACT length of arc AB .

a)

8π cm

b)

6π cm

c)

4π cm

d)

3π cm

e)

Not here

91.

If a circle has a circumference of 10π inches, then its area is

a)

100π in²

b)

25π in²

c)

20π in²

d)

40π in²

e)

Not here

92.

Find the area of the shaded sector of the circle. Leave answer in terms of π

a)

5.83π

b)

43.75π

c)

68.75π

d)

4.58π

93.

What is the area of the shaded sector?

a)

339.12 in²

b)

113.04 in²

c)

339.29 in²

d)

None of the above

94.

Find the area of the sector. Leave your answer in terms of pi.

a)

$7\pi$

b)

$49\pi$

c)

$\frac{7}{4}\pi$

d)

$\frac{49}{4}\pi$

95.

Given the measurements in the diagram, find the total area of the shaded regions.

a)

10.47 cm²

b)

52.36 cm²

c)

26.18 cm²

d)

5.24 cm²

96.

If the measure of arc ABC = 210°, what is the measure of arc AC?

a)

150°

b)

100°

c)

210°

d)

105°

97.

Find the measure of <XTY

a)

65

b)

98

c)

70

d)

52

98.

Solve for x.

a)

x = 11

b)

x = 6

c)

x = 8

d)

x = 9

99.

What is the measure of arc WYZ?

a)

231

b)

255

c)

168

d)

200

100.

What is the arc length of minor arc AB?

a)

5.23

b)

103

c)

33.33

d)

50

101.

In circle O, the radius is 4, and the length of minor arc AB is 4.2 feet. Find the measure of minor arc AB to the nearest degree.

a)

90

b)

60

c)

55

d)

113

102.

a)

26

b)

24

c)

12

d)

18

103.

TS is tangent to circle P. What is x?

a)

11.2

b)

18.0

c)

25.0

d)

30.0

104.

QS is a tangent to circle P. Find QS. (Hint: find the full length of PS first)

a)

144

b)

14

c)

12

d)

13

105.

A point B is 17cm away from the centre O of a circle. AB is the tangent to the circle at A. Given that AB = 15 cm, find the radius of the circle.

a)

8 cm

b)

9 cm

c)

2 cm

d)

16 cm

106.

In the figure,PA and PB are the tangents to a circle of center 'O'. ∠AOB= 120⁰ then ∠APB =

a)

60⁰

b)

30⁰

c)

120⁰

d)

75⁰

107.

In the figure,PA and PB are the tangents to a circle of centre 'O'. If ∠APB = 48⁰ then ∠AOP =

a)

68⁰

b)

66⁰

c)

56⁰

d)

76⁰

108.

Using lines tangent to the circle, find the value of x.

a)

57

b)

137

c)

47

d)

257

109.

Determine if a tangent line is shown in the picture.

a)

Yes

b)

No

c)

Not sure

110.

Determine if a tangent line is shown in the picture.

a)

Yes

b)

No

c)

Not Sture

111.

Determine if a tangent line is shown in the picture.

a)

Yes

b)

No

c)

Note Sure

112.

The polygon circumscribes the circle. Find the perimeter.

a)

78

b)

84

c)

72

d)

86

113.

Point O is the center of each circle. Assume the lines that appear to be tangent are tangent. What is the value of the variable?

a)

26

b)

57

c)

66

d)

114

114.

Find the measure of Angle XTY

a)

65

b)

98

c)

70

d)

52

115.

What is measure of arc PR?

a)

360 degrees

b)

90 degrees

c)

45 degrees

d)

180 degrees

116.

What is m∠ACB?

a)

67.5°

b)

90°

c)

22.5°

d)

45°

117.

a)

A

b)

B

c)

C

d)

D

118.

a)

A

b)

B

c)

C

d)

D

119.

What is the measure of the indicated arc?

a)

70

b)

140

c)

35

d)

90

120.

Find the measure of arc AB.

a)

17

b)

34

c)

68

d)

146

121.

What is the measure of arc FH?

a)

70

b)

35

c)

140

d)

88

122.

What is the measure of angle K and angle M?

a)

$m\angle K=100\ \ \ \ \&\ \ \ m\angle M=100$

b)

$m\angle K=50\ \ \ \ \&\ \ \ m\angle M=50$

c)

$m\angle K=100\ \ \ \&\ \ \ m\angle M=50$

d)

$m\angle K=50\ \ \ \&\ \ \ m\angle M=100$

123.

Find m∠PRQ.

a)

39°

b)

90°

c)

51°

d)

15°

124.

The measure of arc XY is:

a)

54

b)

180

c)

216

d)

74

125.

Find the measure of angle V:

a)

85

b)

80

c)

87

d)

117

126.

Find the measure of arc BC. (Hint: BD is a diameter.)

a)

80

b)

106

c)

104

d)

57

127.

Find the measure of angle H.

a)

40

b)

37

c)

23

d)

26

128.

What is m∠LMO?

(Segment LO is a diameter of Circle P)

a)

30°

b)

45°

c)

180°

d)

90°

129.

Find x.

a)

51

b)

25.5

c)

102

d)

67

130.

Find x.

a)

25

b)

50

c)

12.5

d)

90

131.

Find x.

a)

48

b)

24

c)

96

d)

42

132.

What is the equation to find the inscribed angle?

a)

19x+1=154

b)

19x+1=180

c)

2(19x+1)=154

d)

19x+1+154=360

133.

a)

9

b)

10

c)

11

d)

12

e)

13

134.

a)

5

b)

9

c)

12

d)

16

e)

19

135.

a)

21

b)

22

c)

23

d)

24

e)

25

136.

a)

67

b)

193

c)

281

d)

337

e)

201

137.

Solve for x.

a)

$130\degree$

b)

$260\degree$

c)

$65\degree$

d)

$230\degree$

138.

Solve for x and y.

a)

x=85⁰ y = 150⁰

b)

x = 85⁰ y = 50⁰

c)

x = 95⁰ y = 150⁰

d)

x = 95⁰ y = 50⁰

139.

The diagram shows a semicircle with centre O. Find the value of x.

a)

35

b)

40

c)

45

d)

50

140.

The diagram shows a circle with centre O. The minor arc PQ and the minor arc RS are of equal length. Find the value of x.

a)

20

b)

25

c)

30

d)

35

141.

In the diagram, RST is a straight line. Find the value of x + y.

a)

150

b)

160

c)

170

d)

210

142.

The diagram shows a circle with centre O. Find the value of y.

a)

111

b)

69

c)

55.5

d)

21

Geometry Final Exam Review 2026

Total questions: 142

Worksheet time: 11hrs 35mins

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