Free Printable Geometry Final Exam Review

1.

How is the distance formula correctly written:

a)

$d\ =\ \sqrt{\left(y_{1\ }-\ y_2\right)^2\ -\left(x_{2\ }-\ x_1\right)^2}\$

b)

$d\ =\ \sqrt{\left(x_{2\ }-\ x_1\right)^2\ +\ \left(y_{2_{\ }}-\ y_1\ \right)^2}$

c)

$d\ =\ \sqrt{\left(y_{1\ }-\ y\ _2\right)^2\ +\ \left(x_{2\ }-\ x_1\right)}^2$

d)

d = $\sqrt{\left(x\right)^2-\ \left(y\right)^2}$

2.

Find the distance between the points (4, 3) and (0, 6).

a)

3

b)

4

c)

5

d)

7

3.

Find the distance.

a)

9.7

b)

10.7

c)

11.7

d)

12.7

4.

Find the measure of each angle indicated.

a)

139°

b)

66°

c)

138°

d)

116°

5.

Find the measure of the missing angle.

a)

90^o

b)

10⁰

c)

130^o

d)

50^o

6.

In a triangle, how many total degrees are there?

a)

100%

b)

180 degrees

c)

it varies

d)

360 degrees

7.

Which pair of angles is an example of corresponding angles?

a)

$\angle1\ and\ \angle8$

b)

$\angle3\ and\ \angle7$

c)

$\angle4\ and\ \angle5$

d)

$\angle2\ and\ \angle5$

8.

Which pair of angles is an example of alternate interior angles?

a)

$\angle1\ and\ \angle8$

b)

$\angle3\ and\ \angle7$

c)

$\angle4\ and\ \angle5$

d)

$\angle2\ and\ \angle5$

9.

Which pair of angles is an example of alternate interior angles?

a)

$\angle1\ and\ \angle8$

b)

$\angle3\ and\ \angle7$

c)

$\angle4\ and\ \angle5$

d)

$\angle2\ and\ \angle5$

10.

Find $m\angle1.$

a)

$180\degree$

b)

$65\degree$

c)

$115\degree$

11.

Find $m\angle2.$

a)

$65\degree$

b)

$180\degree$

c)

$115\degree$

12.

Find $m\angle1.$

a)

$131\degree$

b)

$180\degree$

c)

$49\degree$

13.

Find $m\angle2.$

a)

$131\degree$

b)

$180\degree$

c)

$49\degree$

14.

Which statement is NOT true?

a)

Parallel lines have the same slope.

b)

Parallel lines intersect at one point.

c)

Perpendicular lines form a right angle.

15.

If m∠6 = 50^o then m∠4 =

a)

50^o

b)

90^o

c)

130^o

d)

360^o

16.

If the $m\angle7\ =\ 115\degree,$ find the measure of $\angle2.$

a)

$115\degree$

b)

$65\degree$

c)

$180\degree$

d)

Cannot be determined

17.

If the $m\angle5\ =\ 63\degree,$ find the measure of $\angle3.$

a)

$63\degree$

b)

$117\degree$

c)

$180\degree$

d)

Cannot be determined

18.

Find the measure of the missing angle.

a)

100 degrees

b)

67 degrees

c)

113 degrees

19.

Solve for x.

a)

100

b)

20

c)

80

d)

4

20.

What two angles are alternate exterior with angle 4?

a)

∠16

b)

∠15

c)

∠9

d)

∠5

21.

a)

A

b)

B

c)

C

d)

D

22.

a)

A

b)

B

c)

C

d)

D

23.

a)

A

b)

B

c)

C

d)

D

24.

a)

A

b)

B

c)

C

d)

D

25.

a)

A

b)

B

c)

C

d)

D

26.

a)

A

b)

B

c)

C

d)

D

27.

a)

A

b)

B

c)

C

d)

D

28.

a)

A

b)

B

c)

C

d)

D

29.

Find the measure of the indicated angle.

a)

A

b)

B

c)

C

d)

D

30.

Find the measure of the indicated angle.

a)

A

b)

B

c)

C

d)

D

31.

The figures are similar. Find the value of x.

a)

A

b)

B

c)

C

d)

D

32.

Find the values of x and y.

a)

A

b)

B

c)

C

d)

D

33.

The triangles are similar. Find the value of x.

a)

A

b)

B

c)

C

d)

D

34.

Find the measure of angle A.

a)

115

b)

65

c)

32.5

d)

57.5

35.

Find the measure of arc QU

a)

A

b)

B

c)

C

d)

D

36.

Is triangle ABC a right triangle? How do you know?

a)

Yes. Because there's a right angle in the triangle.

b)

No. Because there isn't a right angle at any vertex.

c)

No. Because the sum of the squares of the legs is NOT equal to the square of the hypotenuse.

d)

Impossible to determine.

37.

Compute the perimeter of triangle ABC.

a)

28.73 units

b)

30.11 units

c)

13.3 units

d)

24.03 units

38.

Identify the transformation.

a)

Reflection across y-axis

b)

90 Rotation counter clockwise

c)

Translation 5 units left, 1 unit up.

d)

Translation 5 units right, 1 unit down

39.

Point (7,2) is translated vertically 2 units and horizontally -5 units. Where is the new point located?

a)

(9,-3)

b)

(2,4)

c)

(2,0)

d)

12,4)

40.

Identify the transformation from ABC to A'B'C'.

a)

90^o clockwise rotation

b)

90^o counter clockwise rotation

c)

Reflection across the y-axis

d)

Reflection across the x-axis

41.

a)

x = 22 Degrees

b)

x = 25 Degrees

c)

x = 30 Degrees

d)

x = 33 Degrees

42.

In similar Polygons, corresponding sides are ___ and corresponding angles are ___. (Fill in the blanks)

a)

congruent, proportional

b)

proportional, congruent

c)

congruent, congruent

d)

proportional, proportional

43.

To measure the distance across a pond, a surveyor locates points A, B, C, D, and E as shown. What is AB to the nearest meter?

a)

10

b)

12

c)

15

d)

18

44.

Match the equation with its graph.

a)

b)

c)

d)

45.

Describe the System using the correct option below.

a)

Parallel Lines

b)

Same Line

c)

Intersecting Lines

46.

M is the midpoint. Find AB

a)

24

b)

12

c)

2

d)

48

47.

Solve the missing information.

a)

x=10

y=15

b)

x=56

y=15

c)

X=8

Y=8

d)

x=4

y=4

48.

Solve the missing information.

a)

X=6

Y=12

b)

x=7

y=14

c)

X=24

Y=12

d)

X=5

Y=10

49.

Triangle ABC on a graph has the points A(3,9), B(9,9), and C(3,3). The points and image are dilated by 1/3. What will the new points look like?

a)

A’=(-1,2)

B’=(5,6)

C’=(3,4)

b)

A’=(1,3)

B’=(3,3)

C’=(1,1)

c)

A’=(6,3)

B’=(2,-3)

C’=(-3,-3)

d)

A’=(5,-2)

B’=(-4,-5)

C’=(6,10)

50.

What will the equation look like to find X in the right triangle?

a)

Sin20= x/12

b)

Tan20°= 12/x

c)

cos20°=12/x

d)

Cos=12/20

51.

A 25 foot ladder is leaning against a building. The bottom of the ladder is 7 feet away from the building. How far up the building does the ladder reach?

a)

24 ft

b)

17 ft

c)

30 ft

d)

26 ft

52.

The measures of seven of the interior angles of an octagon are 150°, 100°, 80°, 165°, 118°, 184° and 148°. What is the measure of the eighth interior angle?

a)

924°

b)

516°

c)

135°

d)

156°

53.

If AB = 4, BC = 7, ED = 5, and EC = 13.75, determine whether BD is parallel to AE.

a)

Yes

b)

No

54.

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

55.

Choose the correct scale factor:

a)

2

b)

3

c)

1/3

d)

1/2

56.

Given, "If I have a Siberian Husky, then I have a dog." Identify the inverse.

a)

If I do not have a Siberian Husky, then I do not have a dog.

b)

If I have a dog, then I have a Siberian Husky.

c)

If I do not have a dog, then I do not have a Siberian Husky.

d)

If I do not have a Siberian Husky, then I have a dog.

57.

What is the converse of the following statement?
If it is Saturday, then the school is closed

a)

If the school is closed, then it is Saturday.

b)

If it is not Saturday, then the school is not closed.

c)

If the school is not closed, then it is not Saturday.

58.

Original Statement:
If I am hungry then I will eat a whole pizza.
New Statement:
If I am not hungry then I will eat a whole pizza.

a)

Converse

b)

Inverse

c)

Contrapositive

d)

None of the above

59.

Which of these angles is NOT congruent to angle 5?

a)

Angle 6

b)

Angle 8

c)

Angle 1

d)

Angle 4

60.

A segment has a midpoint of (2,-7) and an endpoint at (8,-5). What are the coordinates of the other endpoint?

a)

(2,10)

b)

(-9,-4)

c)

(5,9)

d)

(-4,-9)

61.

<R & <S are complementary angles. If m<R = (6x-47), and m<S = (x+4), find m<S.

a)

m<S=13

b)

m<S=19

c)

m<S=56

d)

m<S=23

62.

What is the sum of the interior angles of the octagon?

a)

1080°

b)

540°

c)

720°

d)

1440°

63.

What is the measure of angle S?

a)

77°

b)

43°

c)

40°

d)

52°

64.

How can you tell if a triangle is isosceles?

a)

It equals 180°

b)

Each angle is a different measure

c)

All the vertices are congruent

d)

The base angles are congruent

65.

Arrange the measures from greatest to least.

a)

m<k, m<l, m<j

b)

m<l, m<j, m<k

c)

m<j, m<l, m<k

d)

m<l, m<k, m<j

66.

a)

A

b)

B

c)

C

d)

D

67.

The correct way to name the segment is _____

a)

$\overline{EG}$

b)

$\overline{EF}$

c)

$\overline{EFG}$

d)

line E

68.

Which plane is parallel to plane PON?

a)

plane QRN

b)

plane TQM

c)

plane TSR

d)

plane SRN

69.

Which is the correct way to name the angle?

a)

straight angle

b)

$\angle\ ACB$

c)

$\angle\ C$

d)

$\angle\ CBA$

70.

Name the ray in the figure.

a)

$\overrightarrow{AB}$

b)

$\overleftarrow{AB}$

c)

$\overrightarrow{BA}$

d)

$\overline{BA}$

71.

$\overrightarrow{BD\ }$ bisects $\angle\ ABC$ and $m\angle\ ABD\ =\ 32$ , find the measure of $\angle\ ABC$ .

a)

$64\degree$

b)

$52\degree$

c)

$16\degree$

d)

$96\degree$

72.

Are the lines $y=\frac{1}{4}x+3$ and $y=3x-12$ perpendicular? Explain.

a)

Yes, their slpes are equal.

b)

Yes, their slopes are opposite reciprocals

c)

No, their slopes are not equal.

d)

No, their slopes are not opposite reciprocals.

73.

Are the lines $y=-x-4\ and\ y=-x+7$ parallel? Why or why not.

a)

Yes, their slopes are equal.

b)

Yes, their slopes are opposite reciprocals.

c)

No, their slopes are not equal.

d)

No, their slopes are not opposite reciprocals.

74.

Complete the statement:

If a transversal intersects two parallel lines, then ____

a)

corresponding angles are supplementary

b)

same side interior angles are complementary

c)

alternate interior angles are congruent

d)

none of these

75.

True or False:

A trapezoid is a parallelogram.

a)

True

b)

False

76.

True or False

All parallelograms are quadrilaterals.

a)

True

b)

False

77.

True or False

Some parallelograms are rhombuses.

a)

True

b)

False

78.

True or False

The diagonals of a parallelogram always bisect each other.

a)

True

b)

False

79.

What type of triangle is this?

a)

equilateral

b)

scalene

c)

isosceles

d)

right

80.

What type of triangle is this?

a)

equilateral

b)

scalene

c)

isosceles

d)

right

81.

What type of triangle is this?

a)

equilateral

b)

scalene

c)

isosceles

d)

right

82.

Find KL.

a)

18

b)

15

c)

6

d)

20

83.

Solve for x

a)

15

b)

16

c)

18

d)

19

84.

A cruise ship has a large, circular window. It has a diameter of 6 meters. What is the window's area?

a)

31.25 m²

b)

29.55 m²

c)

30.36 m²

d)

28.26 m²

85.

A point that divides, or bisects, a segment into two congruent segments is called a ___________________.

a)

midpoint

b)

congruent segment

c)

angle bisector

d)

endpoint

86.

intersection of l and m

a)

$\cdot$ H

b)

$\cdot$ E

c)

plane Q

d)

$\overleftarrow{F}\overrightarrow{E}$

e)

$\cdot$ D

87.

intersection of plane M and line k

a)

$\overleftarrow{C}\overrightarrow{B}$

b)

$\cdot$ E

c)

j

d)

plane $M$

88.

Are $\cdot$ D and $\cdot$ E collinear?

a)

Yes

b)

No

89.

Draw a conclusion from the statement.
If Jack goes to school, then it is Monday.
Jack doesn't go to school.

a)

Jack skipped school.

b)

It isn't Monday.

c)

It's Saturday.

d)

Invalid

90.

Which law of logic is this?

If I clean the bathroom, then I don't have to do the dishes.

I cleaned the bathroom.

Therefore, I don't have to do the dishes.

a)

Law of Detachment

b)

Law of Syllogism

c)

Law of Contrapositive

d)

None

91.

If we see John on Monday, then we can ask him over for lunch. We see John on Monday.

a)

John may eat with us.

b)

John saw us on Monday

c)

No conclusion can be made since the hypothesis did not occur.

d)

We asked John to have lunch with us.

92.

Using the Law of Syllogism, which of the following completes the statement to form a valid conclusion?
If it is snowing heavily, then school will be canceled.
If school is canceled, the big test will not be given today.
It is snowing heavily, therefore

a)

look out for the snowplows while driving to school.

b)

the big test will not be given today.

c)

the roads will be hard to drive on.

d)

you should call the school to see if school is canceled.

93.

2) Given the following two parallel lines cut by a transversal.

Which pair of angles represents corresponding angles?

a)

$\angle1$ and $\angle6$

b)

$\angle6$ and $\angle5$

c)

$\angle7$ and $\angle8$

d)

$\angle4$ and $\angle8$

94.

Find the missing side using proportions.

a)

a

b)

b

c)

c

d)

d

95.

Find the missing side using proportions.

a)

a

b)

b

c)

c

d)

d

96.

Nelly is building a skate ramp. If the height of the ramp is 5 ft and the angle of the ramp from the ground is 15⁰, how long is the ramp?

(hint: the length of the ramp will be the hypotenuse SOH-CAH-TOA)

a)

5.17

b)

18.7

c)

19.3

d)

.05

97.

Find the exact values of x and y

a)

x= 4, y= 8

b)

x= 8, y= 12

c)

x= 4, y= 12

d)

x= 4√3, y= 8

98.

Find x.

a)

$\sqrt{28}$

b)

14

c)

10

d)

$\sqrt{14}$

99.

Find the area.

a)

472in²

b)

944in²

c)

475in²

d)

645in²

100.

Find the area of the parallelogram

a)

A = 13 m

b)

A = 20 m²

c)

A = 50 m

d)

A = 40 m²

101.

Which method can be used to prove the triangles are similar?

a)

AA~

b)

SSS~

c)

SAS~

d)

Not Similar

102.

What is the measure of angle PNQ?

a)

70^o

b)

35^o

c)

45^o

d)

90^o

103.

a)

90^o

b)

180^o

c)

100^o

d)

80^o

104.

Find the length of CF.

a)

8

b)

4

c)

3

d)

6

105.

a)

15^o

b)

30^o

c)

60^o

d)

120^o

106.

∠1 and ∠2 are ... ? (Choose ALL that apply.)

a)

vertical

b)

supplementary

c)

a linear pair

d)

adjacent

107.

The two triangles shown are congruent by what property ?

a)

SSS

b)

SAS

c)

ASA

d)

AAS

e)

HL

108.

Are these two triangles similar ?

If yes, by what property ?

a)

No they cannot be proven similar.

b)

Yes, by SSS

c)

Yes, by SAS

d)

Yes, by AA

109.

What equation would you use to find x ?

a)

cos 55° = (x/29)

b)

tan 55° = (29/x)

c)

29² + x² = 55²

d)

tan 55° = (x/29)

110.

Which inverse function would you use to find x ?

a)

sin

b)

cos

c)

tan

111.

What is the circumference of this circle ?

a)

66 ft²

b)

346 ft

c)

66 ft

d)

132 ft

112.

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

113.

What are three collinear points.

a)

G,H and F

b)

E, D and G

c)

E, G and H

d)

D, E and F

114.

Name three coplanar points.

a)

G, D and E

b)

D, E and H

c)

F, H and G

d)

G, E and H

115.

How many planes are on the figure?

a)

4

b)

8

c)

6

d)

12

116.

Which similarity theorem or postulate you use to determine whether the triangles are similar.

a)

Side-Side-Side(SSS)

b)

Side-Angle-Side (SAS)

c)

Angle-Angle (AA)

d)

Angle-Side-Angle (ASA)

117.

State the similarity theorem or postulate you would use to determine whether the triangles are similar.

a)

Angle-Angle (AA)

b)

Side-Angle-Side (SAS)

c)

Side-Side-Side (SSS)

d)

Angle-Side-Angle (ASA)

118.

State the similarity theorem or postulate you would use to determine whether the triangles are similar.

a)

Angle-Angle (AA)

b)

Side-Angle-Side(SAS)

c)

Side-Side-Side(SSS)

d)

Angle-Side-Angle (ASA)

119.

Congruent by

a)

SSS

b)

SAS

c)

ASA

d)

AAS

120.

Congruent by

a)

SSS

b)

SAS

c)

ASA

d)

AAS

121.

Congruent by

a)

SSS

b)

SAS

c)

ASA

d)

AAS

122.

Congruent by

a)

SSS

b)

SAS

c)

ASA

d)

AAS

123.

Find the exterior angle

a)

100

b)

55

c)

45

d)

80

124.

The figure is an example of a(n) ...

a)

angle bisector

b)

midsegment

c)

altitude

d)

median

125.

The figure is an example of a(n) ...

a)

angle bisector

b)

perpendicular bisector

c)

median

d)

midsegment

126.

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

a)

Yes

b)

No

c)

Maybe

d)

Pythagoras

127.

What is the ratio for Cosine?

a)

Opp/Hyp

b)

Opp/Adj

c)

Adj/Opp

d)

Adj/Hyp

128.

What is the ratio for Tangent

a)

Opp/Adj

b)

Adj/Opp

c)

Opp/Hyp

d)

Hyp/Opp

129.

What is the ratio for Sine?

a)

Hyp/Opp

b)

Opp/Hyp

c)

Opp/Adj

d)

Adj/Opp

130.

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

131.

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

132.

Solve for the missing angle

a)

50

b)

0.053

c)

36.9

d)

95

133.

To find the height of a very tall pine tree, you place a mirror on the ground and stand where you can see the top of the pine tree. How tall is the tree?

a)

144 feet

b)

72 feet

c)

36 feet

134.

a)

20

b)

30

c)

25

d)

23

135.

What is the measure of angle A?

a)

34°

b)

180°

c)

112°

d)

79°

136.

Find the given angle.

a)

59°

b)

78°

c)

43°

d)

242°

137.

Determine the measure of ∠NOP

a)

15°

b)

20°

c)

40°

d)

50°

138.

Determine the measure of ∠UVS

a)

19.5°

b)

39°

c)

78°

d)

102°

139.

$\angle1$ and $\angle2$ are ___.

a)

Alternate Interior Angles

b)

Alternate Exterior Angles

c)

Same-side Interior Angles

d)

Corresponding Angles

e)

None of these

140.

$\angle7\$ and $\angle5$ are ___.

a)

Alternate Interior Angles

b)

Alternate Exterior Angles

c)

Same-side Interior Angles

d)

Corresponding Angles

e)

None of these

141.

$\angle4$ and $\angle8$ are ___.

a)

Alternate Interior Angles

b)

Alternate Exterior Angles

c)

Same-side Interior Angles

d)

Corresponding Angles

e)

None of these

142.

A region bounded by an arc and its chord is a

a)

sector of a circle

b)

arc of a circle

c)

arc length of a circle

d)

segment of a circle

143.

Given that the triangles are similar which 2 proportions can be used to find n?

a)

n/21 = 9/14

b)

n/21 = 14/9

c)

n/9 = 14/21

d)

n/14 = 9/21

e)

n/9 = 21/14

144.

Given that the triangles are similar, find the value of n rounded to the nearest tenth

a)

14.5

b)

14.0

c)

13.5

d)

13.0

e)

12.5

145.

What is the equation of the circle that has a radius of 4 and is centered at (-5, -3)?

a)

(x + 5)² + (y + 3)² = 16

b)

(x + 5)² + (y + 3)² = 4

c)

(x - 5)² + (y - 3)² = 16

d)

(x - 5)² + (y - 3)² = 4

146.

Given that cos (51) = 16/w can used to find w, what calculation should be used?

a)

w = 16 ⋅ cos (51)

b)

w = 16 / cos(51)

147.

What trig ratio can be used to find the angle the ladder makes with the ground "g"?

a)

sin(g) = 1.41/2.21 so sin^-1(1.41/2.21)

b)

cos(g) = 1.41/2.21 so cos^-1(1.41/2.21)

c)

tan(g) = 1.41/2.21 so tan^-1(1.41/2.21)

d)

tan(g) = 2.21/1.41 so tan^-1(2.21/1.41)

148.

Rotation Rules (clockwise):

180^o rotation: (x, y)→(-x, -y)

What are the coordinates of C' after a rotation of 180° clockwise?

a)

(-3, -1)

b)

(3,1)

c)

(1,3)

d)

(-1, -3)

149.

Describe if the following triangles are congruent by choosing the appropriate postulate to support your answer.

a)

Not congruent

b)

SAS

c)

SSS

d)

ASA

150.

Describe if the following triangles are congruent by choosing the appropriate postulate to support your answer.

a)

Not Congruent

b)

SSS

c)

ASA

d)

SAS

Geometry Final Exam Review

Total questions: 150

Worksheet time: 38hrs 30mins

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