Free Printable Geometry Final Exam Review

1.

Find the volume of the conical figure. Round to the nearest hundredth.

a)

14.13 in³

b)

56.55 in³

c)

169.65 in³

d)

113.10 in³

2.

Barney wanted to know how much ice cream he got in one scoop. The radius of a scoop is 2 inches. Find the volume. Use 3.14 for pi.

a)

345.3 in³

b)

33.5 in³

c)

25.1 in³

d)

50.2 in³

3.

The definition of a circle is

a)

set of all points in a plain that are the same distance from a point called the center

b)

the distance around a share

c)

a large figure

d)

a pizza, orange, plum, or watermelon

4.

How many degrees are in a circle?

a)

90

b)

180

c)

270

d)

360

5.

a)

A

b)

B

c)

C

d)

D

6.

A ____ angle is an angle whose vertex is a the center of a circle.

a)

supplementary

b)

complimentary

c)

central

d)

obtuse

7.

a)

a

b)

b

c)

c

d)

d

8.

a)

a

b)

b

c)

c

d)

d

9.

a)

a

b)

b

c)

c

d)

d

10.

a)

a

b)

b

c)

c

d)

d

11.

a)

a

b)

b

c)

c

d)

d

12.

a)

a

b)

b

c)

c

d)

d

13.

a)

19^o

b)

20^o

c)

85^o

d)

95^o

14.

The value of x is

a)

65^o

b)

48^o

c)

13^o

d)

142^o

15.

What is the area of the shaded region in the figure at right?

a)

1

b)

2

c)

4

d)

6

16.

The area of the trapezoid shown to the right is found by

a)

$\frac{1}{2}\left(12+6\right)\left(8\right)$

b)

$\left(16\right)\left(7\right)$

c)

$\frac{1}{2}\left(12+6\right)\left(7\right)$

d)

$\frac{1}{2}\left(\frac{12+6}{2}\right)\left(7\right)$

17.

a)

$y=-\frac{2}{3}x+6$

b)

$y=-\frac{2}{3}x+5$

c)

$y=-\frac{3}{2}x-2$

d)

$y=\frac{3}{2}x-6$

18.

$Given\ \angle1\cong\angle2,\ which\ theorem\ could\ be\ used\ to\ show\ that\ \Delta ABN\sim\Delta YXN$

a)

AA

b)

SAS

c)

SSS

d)

ASA

19.

Given 3x – 2y = – 12.

A line parallel is

a)

$y=\frac{2}{5}x-7$

b)

$y=\frac{3}{2}x+5$

c)

$y=-\frac{2}{3}x+8$

d)

$y=-\frac{3}{2}x+1$

20.

What is the measure of angle PNQ?

a)

70^o

b)

35^o

c)

45^o

d)

90^o

21.

a)

90^o

b)

180^o

c)

100^o

d)

80^o

22.

Find the length of CF.

a)

8

b)

4

c)

3

d)

6

23.

a)

15^o

b)

30^o

c)

60^o

d)

120^o

24.

a)

25.0 m²

b)

27.93 m²

c)

6.98 m²

d)

50.0 m²

25.

What is the volume of the cone?

a)

320π

b)

363π

c)

1280π

d)

960π

26.

a)

The cylinders have different volumes because they have different radii

b)

The cylinders have different volumes because they have different surface areas.

c)

The cylinders have the same volume because the washers are solid

d)

The cylinders have the same volume because they have the same cross-sectional area at every plane parallel to the bases.

27.

Which point is on a circle with a center of (3,-9) and a radius of 5?

a)

(-6,5)

b)

(-1,6)

c)

(1,6)

d)

(6,-5)

28.

Find the coordinates of P so that P partitions the segment AB in the ratio 1 to 3 if A (-5,4) and B(7,-4).

a)

(-2,2)

b)

(-1,1)

c)

(-8, 8)

d)

(2,-2)

29.

Find the measure of ∠QRS.

a)

6^o

b)

115^o

c)

65^o

d)

119^o

30.

Find the midpoint between G( -1, 2) and H( -3, - 4)

a)

$\left(\frac{1}{2},-\frac{7}{2}\right)$

b)

$\left(-2,-1\right)$

c)

$\left(-4,-2\right)$

d)

$\left(1,3\right)$

31.

Which coordinate notation represents the translation?

a)

$\left(x,\ y\right)\rightarrow\left(x-5,y-7\right)$

b)

$\left(x,\ y\right)\rightarrow\left(x+6,y+4\right)$

c)

$\left(x,\ y\right)\rightarrow\left(x+5,y+7\right)$

d)

$\left(x,\ y\right)\rightarrow\left(x-4,y-6\right)$

32.

Solve for x

a)

19

b)

6

c)

38

d)

32

33.

Which of the following can be used to prove the triangles congruent?

a)

SSS

b)

ASA

c)

SAS

d)

SSA

34.

Find the value of x.

a)

10

b)

29

c)

23

d)

35

35.

Which of the following sets of angle measures could be the 3 interior angles of a triangle? Choose all that apply.

a)

$75\degree,\ 80\degree,\ 25\degree$

b)

$40\degree,\ 40\degree,\ 90\degree$

c)

$30\degree,\ 60\degree,\ 90\degree$

d)

$10\degree,\ 20\degree,\ 150\degree$

36.

a)

( - 2, 2)

b)

( - 6, - 6)

c)

( - 5, 1)

d)

(5, -1)

37.

a)

$\sqrt{106}$

b)

$\sqrt{8}$

c)

$\sqrt{14}$

d)

$\sqrt{10}$

38.

A(3,1) B(-2,-1) written correctly is:

a)

$\sqrt{\left(-2-3\right)^2\ +\ \left(-1-1\right)^2}$

b)

$\sqrt{\left(1-3\right)^2\ +\ \left(-1-2\right)^2}$

c)

$\sqrt{\left(-2-3\right)^2\ -\ \left(-1-1\right)^2}$

d)

$\sqrt{\left(-2-3\right)^2\ -\ \left(-1-1\right)^2}$

39.

What type of angles are these?

a)

Adjacent Angles

b)

Linear Pair

c)

Complementary Angles

d)

Supplementary Angles

e)

Vertical Angles

40.

a)

A

b)

B

c)

C

d)

D

41.

Use the congruency statement to answer the following:
<F = ___

a)

<H

b)

<I

c)

<G

d)

not congruent to another angle

42.

If ∆MNO ≅ ∆PQR, which of the following can you NOT conclude as being true? [Hint: DRAW A PICTURE!!]

a)

MN = PR

b)

∠M ≅ ∠P

c)

NO = QR

d)

∠N ≅ ∠Q

43.

Choose the correct scale factor:

a)

2.5

b)

1.5

c)

3.5

d)

4

44.

Does a triangle with these side lengths exist?
15, 12, 9

a)

Yes

b)

No

c)

I don't know.

45.

Complete the Theorem:

"The sum of the measures of the two smallest sides of a triangle...

a)

...will equal the measure of the third side.

b)

...cannot be more than the measure of the third side.

c)

...must be greater than the measure of the third side.

d)

...has nothing to do with the third side.

46.

Find the interior angle sum for each polygon. Round your answer to the nearest tenth if

necessary.

a)

A

b)

B

c)

C

d)

D

47.

Find the value of X

a)

94

b)

25

c)

36

d)

180

48.

The opposite angles of a parallelogram are ...

a)

complementary

b)

congruent

c)

supplementary

d)

perpendicular

49.

In a parallelogram, consecutive angles are __________.

a)

congruent

b)

supplementary

c)

corresponding

d)

parallel

50.

In a parallelogram, diagonals are __________.

a)

perpendicular

b)

bisected

c)

congruent

d)

parallel

51.

Find the measure of the midsegment XY:

a)

21

b)

9

c)

12

d)

10.5

52.

Which of the following statements are true?

a)

BD and AC are perpendicular

b)

BD and AC are congruent

c)

∠A and ∠C are congruent

d)

AD and DC are congruent

53.

What is the final step in solving this work for c?
a² + b² = c²
3² + 4² = c²
9 + 16 = c²
25 = c²

a)

Divide both sides by 2

b)

Take the square root of both sides

54.

Find m∠PRQ.

a)

39°

b)

90°

c)

51°

d)

15°

55.

Which shows a tangent line?

a)

b)

c)

d)

56.

Graph the image of the figure using the transformation given.

a)

b)

c)

d)

57.

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

a)

4√2

b)

4

c)

8

d)

4√3

58.

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

59.

A 30 ft. wire stretches from the top of a light pole diagonally to the ground. The light pole is 10 feet high. What is the angle the wire makes with the ground?

a)

66 degrees

b)

80 degrees

c)

30 degrees

d)

19 degrees

60.

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

a)

63.6 ft

b)

1.59 ft

c)

74.2 ft

d)

86.9 ft

61.

Find the measure of each side indicated. Round to the nearest tenth.

a)

2.1

b)

1

c)

0.6

d)

1.4

62.

Find the measure of each side indicated. Round to the nearest tenth.

a)

2.1

b)

1

c)

1.7

d)

0.5

63.

What is the distance between (-5, 3) and (4, -5)?

a)

$\sqrt{128}$

b)

$\sqrt{145}$

c)

$\sqrt{113}$

d)

$\sqrt{130}$

64.

Find the missing length indicated. Round your answer to the nearest whole number.

(a)

65.

What is the reasoning for the 3rd statement?

a)

Reflexive

b)

definition of bisector

c)

Alternate interior angles

d)

SAS

66.

Solve for Angle 1 and Angle 2.

a)

$\angle1=92\degree,\ \angle2=46\degree$

b)

$\angle1=118\degree,\ \angle2=118\degree$

c)

$\angle1=92\degree,\ \angle2=92\degree$

d)

$\angle1=136\degree,\ \angle2=136\degree$

67.

Find the area of the kite in square feet.

(a)

68.

$\angle QRT$ and $\angle TRS$ are supplementary. Solve for x.

a)

12

b)

15

c)

9

d)

3

69.

a)

a

b)

b

c)

c

d)

d

70.

What is the value of x?

a)

2

b)

18

c)

2√9

d)

9√2

71.

Find $\tan\theta$ .

a)

$\tanθ=\frac{5}{13}$

b)

$\tan\theta=\frac{12}{13}$

c)

$\tan\theta=\frac{12}{5}$

d)

$\tan\theta=\frac{5}{12}$

72.

Find the area

a)

96 cm²

b)

48 cm²

c)

36 cm²

d)

48 cm

73.

Find the area of the shaded region.

a)

13.5

b)

54

c)

67.5

d)

13.5

74.

What is the image of J (8, -6) after a rotation of 180° counterclockwise?

a)

J' (8, 6)

b)

J' (-6, 8)

c)

J' (-8, 6)

d)

J ' (-8, -6)

75.

Triangular Prism with base lengths 3 m, 4 m, 5 m, and a height of 6m. What is the surface area?

a)

84 m²

b)

92 m²

c)

102 m²

d)

96 m²

76.

a)

278⁰

b)

297⁰

c)

90⁰

d)

105⁰

77.

Given that B and D are points of tangency to circle with center at C. What is the value of x? Select all the correct answers.

a)

1

b)

-1

c)

3

d)

-3

78.

The two square pyramids are similar. The side length of the smaller pyramid is $\frac{3}{4}$ the side length of the larger pyramid.

Which fraction represents the ratio of the base area of the smaller pyramid to the base area of the larger pyramid?

a)

$\frac{16}{9}$

b)

$\frac{3}{4}$

c)

$\frac{4}{3}$

d)

$\frac{9}{16}$

79.

An equilateral triangle has an apothem measuring 2.16 cm and a perimeter of 22.45 cm.

What is the area of the equilateral triangle, rounded to the nearest tenth?

a)

$2.7\ cm^2$

b)

$4.1\ cm^2$

c)

$16.2\ cm^2$

d)

$24.2\ cm^2$

80.

In the parallelogram shown, $AE\ =\ t+2$ , $CE=3t-14$ , and $DE=2t+8$ .

What is the length of line segment DB?

a)

20 units

b)

24 units

c)

48 units

d)

68 units

81.

The equation $\sin\left(25\degree\right)=\frac{9}{c}$ can be used to find the length of $\overline{AB}$ .

What is the length of

\overline{AB}

? Round to the nearest tenth.

a)

19.3 in

b)

21.3 in

c)

23.5 in

d)

68.0 in

82.

What is the length of $\overline{SR}$ ?

a)

15 units

b)

18 units

c)

12 units

d)

9 units

83.

A _______ is the locus or set of all points a plane equidistant from a given point called the _____ of the circle.

(a)

84.

What is the volume formula for a prism?

a)

V=PL

b)

V=Bh

c)

V=LWH

85.

What is the correct angle measure of x?

a)

260

b)

100

c)

70

d)

80

86.

a)

6

b)

24

c)

36

d)

12

87.

Which of the following is NOT an acceptable way to prove triangles congruent?

a)

SSS

b)

ASA

c)

AAA

d)

SAS

88.

The diagonals of the rhombus are: d1 = 8.6 mm and 10.2 mm. Find the area:

a)

43.9 squared millimeters

b)

87.7 squared millimeters

c)

37.7 squared millimeters

d)

18.8 squared millimeters

89.

Find the volume of this rectangular pyramid.

a)

364 cm³

b)

1092 cm³

c)

546 cm³

d)

182 cm³

90.

Which of the following is the definition of collinear?

a)

Points that lie on the same line.

b)

A segment that bisects an angle.

c)

A segment starting at the vertex of a triangle and intersecting the midpoint of the opposite side.

d)

A triangle with one obtuse angle.

91.

Which of the following is the definition of supplementary.

a)

Two angles with a sum of 180.

b)

Two lines that intersect to make a 90 angle.

c)

A point that divides a segment into two congruent parts.

d)

A triangle with one obtuse angle.

92.

Which of the following is the definition of a median?

a)

A triangle with one right angle.

b)

A point that divides a segment into two congruent parts.

c)

A triangle with three congruent sides.

d)

A segment starting at the vertex of a triangle and intersecting the midpoint of the opposite side.

93.

Find the value of x in the diagram.

a)

10

b)

4

c)

6

d)

7

94.

Find the value of x and y.

a)

x = 14, y = 37

b)

x = 37, y = 14

c)

x = 14, y = 6

d)

x = 6, y = 14

95.

Find the value of x in the diagram.

a)

61

b)

73

c)

46

d)

67

96.

The exterior angles of a polygon add up to __________________.

a)

180

b)

(n - 2)*180

c)

360

d)

(n - 2)*360

97.

The interior angles of a polygon add up to equal ___________________.

a)

360

b)

(n - 2)*180

c)

(n - 2)*360

d)

180

98.

What is reason 2?

a)

Given

b)

Addition Property of Equality

c)

Subtraction Property of Equality

d)

Substitution Property of Equality

99.

Identify which sequence of rigid motions maps ∆ABC onto ∆A'B'C' and then maps ∆A'B'C' onto ∆A''B''C''.

a)

a rotation followed by another rotation

b)

a translation followed by a reflection

c)

a reflection followed by a translation

d)

a reflection followed by a rotation

100.

Which sequence of transformation maps figure 1 onto figure 2 and then figure 2 onto figure 3?

a)

a reflection followed by a translation

b)

a rotation followed by a translation

c)

a translation followed by a reflection

d)

a translation followed by a rotation

101.

Which sequence of transformations maps ∆ABC onto ∆DEF?

a)

a reflection over the x-axis followed by a translation

b)

a reflection over the y-axis followed by a translation

c)

a rotation of 180˚ about the origin followed by a translation

d)

a counterclockwise rotation of 90˚ about the origin followed by a translation

102.

The vertices of ∆JKL have coordinates J (5 , 1) , K (-2, -3), L (-4, 1). Under which transformation is the image ∆J'K'L' NOT congruent to ∆JKL?

a)

a translation of two units to the right and two unit down

b)

a counterclockwise rotation of 180˚ around the origin

c)

a reflection over the x-axis

d)

a dilation with a scale factor of 2 and centered at the origin.

103.

What is this picture representing?

a)

Parallel Lines

b)

Perpendicular lines

c)

Congruent Segments

d)

Angle

104.

In the following image, the segment with endpoints D and K rotates 90^° counterclockwise around the origin to which segment ?

a)

The segment with endpoints D and K.

b)

The segment with endpoints H and J.

c)

The segment with endpoints F and L.

d)

The segment with endpoints B and J.

105.

Reflect the quadrilateral with vertices: (3,-3), (3,15), (-8,-3), and (-8,15) over the line y = -5.

a)

Quadrilateral with vertices: (-3,-3), (15,3), (-3,-8),(15,-8)

b)

Quadrilateral with vertices: (3,-7), (3,-25), (-8,-7), (-8,-25)

c)

Quadrilateral with vertices: (-13,-3), (-13,15), (-2,-3), (-2,15)

d)

Quadrilateral with vertices: (-7,-13), (-25,-13), (-7,-2), (-25,-2)

106.

a)

64

b)

4

c)

1/4

d)

17/4

107.

Find the missing length.

a)

21

b)

18

c)

16

d)

24

108.

Set up the problem so that you can solve for X.

a)

sin X = 41/28

b)

tan X = 41/28

c)

cos X = 28/41

d)

sin X = 28/41

109.

State if the triangle is acute, obtuse, or right.

a)

acute

b)

obtuse

c)

right

110.

What is the area of the shaded region?

a)

50.27 units²

b)

3015.93 units²

c)

8.38 units²

d)

4.19 units²

111.

Find the arc length.

a)

5.50 cm

b)

11.00 cm

c)

0.39 cm

d)

141.37 cm

112.

Find the sum of the measures of the angles of the figure.

a)

1260

b)

1440

c)

1620

d)

320

113.

Write the equation of a circle whose center is (-3, 4) and the radius is 9.

a)

(x - 3)² + (y + 4)² = 9

b)

(x + 3)² + (y - 4)² =9

c)

(x - 3)² + (y + 4)² = 81

d)

(x + 3)² + (y - 4)² = 81

114.

What is the converse to this statement?

a)

If it isn't dark outside, then it is not night.

b)

If it is night, then it is dark outside

c)

If it is not night, then it is not dark outside.

d)

It is night.

115.

What is the inverse to this statement?

a)

If you live in Canada, you live in Montreal

b)

If you don't live in Montreal, then you don't live in Canada.

c)

If you don't live in Canada, you don't live in Montreal.

d)

Montreal is in Brazil.

116.

What is this mean?

a)

Conditional Statement

b)

Converse

c)

Inverse

d)

Contrapositive

117.

What is this?

a)

Conditional Statement

b)

Inverse

c)

Converse

d)

THIS IS A GEOMETRY CLASS!!! GIVE ME NUMBERS!

118.

What is the contrapositive to this?

a)

If the food is not cooked, then it is not in the oven.

b)

If the food is not in the oven, then it is not cooked.

c)

If the food is cooked, then its in the oven.

d)

If food is not in the oven, then its cooked.

119.

Conditional: If Maria gets married, then the reception will be at the country club.
What is this statement: If the reception is at the country club, then Maria will be getting married.

a)

Converse

b)

Inverse

c)

Contrapositive

d)

Negation

120.

This symbol, ↔, means?

a)

and

b)

or

c)

if and only if

d)

implies

121.

What is the conclusion that you can infer from these two premises below:

All tigers are cat

All cats are animals

Therefore .................................

a)

Cat are tigers

b)

Animals are cats

c)

All tigers are animals

d)

Cat are tigers

122.

If possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.

Conditional: If two lines do not intersect, then they are coplanar and parallel, or skew.

Premise: Lines AB and CD do not intersect.

a)

Lines AB and CD are parallel and not coplanar.

b)

Lines AB and CD are skew.

c)

Lines AB and CD are parallel and coplanar or they are skew.

d)

No Conclusion can be made.

123.

a)

A

b)

B

c)

C

d)

D

124.

In the diagram, a tangent and a line drawn to the point of tangency form a right triangle. Solve for "?" (the length of the hypotenuse)

a)

15

b)

6

c)

-24

d)

14

125.

What is the value of x?

a)

A

b)

B

c)

C

d)

D

126.

Find the perimeter of the polygon.

a)

77.8

b)

73.4

c)

78.8

d)

67.4

127.

a)

A

b)

B

c)

C

d)

D

128.

Determine the value of x using the information in the diagram.

a)

60º

b)

70º

c)

80º

d)

100º

129.

What is the equation of the circle?

a)

(x+1)² + (y +1)² = 3

b)

(x+1)² + (y -1)² = 3

c)

(x+1)² + (y +1)² = 9

d)

(x-1)² + (y -1)² = 9

130.

Pick the correct Similarity Statement for the Triangles shown.

a)

ΔCAB ~ ΔDEF

b)

ΔABC ~ ΔDFE

c)

ΔABC ~ ΔDEF

d)

ΔBCA ~ ΔDEF

131.

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

a)

equal

b)

congruent

c)

proportional

d)

none of these

132.

Find the missing length. (Hint: Set up your proportion and solve for x.)

a)

21

b)

18

c)

16

d)

24

133.

Set up an equation that could be used to solve for the variable. (Hint: SOH CAH TOA)

a)

b)

c)

d)

134.

Given the isosceles triangle, find the value of x.

(Input just the number for x)

(a)

135.

Name the angles from BIGGEST to SMALLEST

a)

R, S, T

b)

S, T, R

c)

S, R, T

d)

T, S, R

136.

Given the Parallelogram: Find the value of x and y.

a)

x = 4, y = 4

b)

x = 4, y = 116

c)

x = 3, y = 116

d)

x = 116, y = 116

137.

Find the value of x.

(Input just the number for x)

(a)

138.

Solve for x, then find the measure of $\angle F$

a)

46

b)

5

c)

90

d)

1.8

139.

A ladder leans against a brick wall. The foot of the ladder is 6 feet from the wall. The ladder reaches a height of 15 feet on the wall. Find to the nearest degree, the angle the ladder makes with the wall.

a)

$22\degree$

b)

$66\degree$

c)

$24\degree$

d)

$37\degree$

140.

Identify the 3D figure.

a)

A

b)

B

c)

C

d)

D

141.

Identify the 3D figure.

a)

A

b)

B

c)

C

d)

D

142.

Find m∠BAD.

(a)

143.

In ∆ABC, N is the incenter, NE = 8x - 9 and ND = 3x + 6. What is the measure of NF?

(a)

144.

In ∆LMN, point P is the centroid, and BP = 3. Find LP.

(a)

145.

In ∆LMN, point P is the centroid, and BP = 3. Find BL.

(a)

146.

The perpendicular bisectors of ∆ABC intersect at point G. Find the measure of AG.

(a)

147.

You install fencing around your large triangular garden. Then you divide it into four small triangular gardens by connecting the midpoints of each side of the triangle with fencing. How many feet of fencing do you need for the entire project?

(a)

148.

List the sides of ∆ABC from shortest to longest.

a)

AB, CB, AC

b)

AB, AC, CB

c)

CB, AB, AC

d)

CB, AC, AB

149.

a)

SSS~

b)

SAS~

c)

AA~

d)

Not Similar

150.

State if the two triangles are congruent.

If they are, state by which postulate or theorem they are congruent.

If they are not, state "not congruent".

a)

Yes, SAS

b)

Yes, AAS

c)

Yes, SSA

d)

Yes, HL

e)

No, Not Congruent

151.

What is reason #3?

a)

Given

b)

Substitution Property

c)

Addition Property

d)

Segment Addition Property

152.

Solve for x.

a)

29

b)

33

c)

41.5

d)

50

153.

Find h

a)

35.60

b)

35.00

c)

35.71

d)

61.03

154.

What's x?

a)

1080°

b)

45°

c)

135°

d)

1440°

Geometry Final Exam Review

Total questions: 154

Worksheet time: 7hrs 32mins

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