Free Printable Review Geometry CBE

1.

Write the equation of the perpendicular bisector of the line AB given:
A(3,-3) & B(1,-1)

a)

y = x - 4

b)

y = x + 4

c)

y = 1/2x -4

d)

y = x + 2

2.

Write the equation of the perpendicular bisector of the line AB given:
A(1,3) & B(-3,5)

a)

y = 2x + 4

b)

y = 2x + 6

c)

y = -2x + 6

d)

y = 2x - 6

3.

Given are the lengths of two sides of a triangle. Find the range of lengths for the third side. 7 ft, 13 ft

a)

more than 6 but less than 20

b)

more than 20 but less than 6

c)

less than 6 but more than 20

4.

Given are the lengths of two sides of a triangle. Find the range of lengths for the third side. 7 mm, 4 mm

a)

more than 3 but less than 11

b)

more than 11 but less than 3

c)

less than 3 but more than 11

5.

What missing piece of information is needed to prove the triangles congruent using ASA?

a)

GC = CD

b)

CE = CD

c)

∠GCE≅∠BCE

d)

BD = GE

6.

What missing piece of information is needed to prove the triangles congruent using SAS?

a)

NM = AM

b)

NL = CA

c)

∠M≅∠B

d)

∠N≅∠C

7.

What missing piece of information is needed to prove the triangles congruent using SAS?

a)

∠F≅∠Q

b)

∠G≅∠R

c)

∠H≅∠S

d)

FH = QS

8.

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

a)

SSS

b)

ASA

c)

AAS

d)

Not Possible

9.

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

a)

SAS

b)

ASA

c)

SSS

d)

Not Possible

10.

a)

Congruent by HL

b)

Congruent by SAS

c)

Congruent by SSS

d)

Not Necessarily Congruent

11.

What does deductive reasoning use to form its arguments?

a)

patterns

b)

specific cases

c)

observed examples

d)

facts, definitions, accepted properties, and laws of logic

12.

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, then...

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.

13.

p→q
q→r
∴p→r
Which law is modeled?

a)

Law of Syllogism

b)

Law of Detachment

c)

Law of Contrapositive

d)

Law of Shannon

14.

Use Law of Syllogism to make a conclusion.
If a number is divisible by 10, then it is divisible by 2. If a number is divisible by 2, then it is even.

a)

If a number is divisible by 10, then it is even,

b)

If a number is even, then it is divisible by 10.

c)

If a number is divisible by 2, then it is even.

d)

If a number is even, then it is divisible by 2.

15.

It is dangerous to drive on icy streets. The streets are icy now so it is dangerous to drive now.

a)

Deductive

b)

Inductive

16.

Snakes are reptiles and reptiles are cold blooded; therefore, snakes are cold blooded.

a)

Deductive

b)

Inductive

17.

Obtuse angles are greater than 90 degrees. This angle is 110 degrees, so it is obtuse.

a)

Deductive

b)

Inductive

18.

Angles a & o, a & b, a & m in that order

a)

Supplemental, Vertical, Alternate Interior

b)

Vertical, Corresponding, Alternate Exterior

c)

Alternate Exterior, Same Side Interior, Corresponding

d)

Vertical, Supplemental, Alternate Exterior

19.

What kind of relationship is between 1 & 12?

a)

Alternate Interior

b)

Vertical

c)

Alternate Exterior

d)

Corresponding

20.

If a & b are parallel and c & d are parallel and angle 2 is 65 degrees, what is angle 15?

a)

105

b)

15

c)

65

d)

115

21.

What is the measure of x?

a)

101°

b)

111°

c)

121°

d)

131°

22.

Solve for x

a)

48

b)

85

c)

24

d)

9

23.

Find the measure of the indicated angle.

a)

38 degrees

b)

43 degrees

c)

22 degrees

d)

76 degrees

24.

Find the measure of the indicated angle.

a)

35 degrees

b)

40 degrees

c)

25 degrees

d)

30 degrees

25.

Find the measure of angle A.

a)

21 degrees

b)

31 degrees

c)

128 degrees

d)

24 degrees

26.

What is the value of y?

a)

7

b)

4

c)

6

d)

14

27.

What is the length of side JK?

a)

12

b)

30

c)

33

d)

3

28.

What is the length of DF?

a)

8

b)

4

c)

25

d)

71

29.

Lines L and M are parallel. Find x. Enter a number only.

(a)

30.

Lines L and M are parallel. Find x. Enter a number only.

(a)

31.

Lines L and M are parallel. Find x. Enter a number only.

(a)

32.

Given that P(-4, -2), Q(-2, 2) and R(5, 1) are vertices of a triangle, calculate the perimeter and classify the triangle.

a)

21.1, Isosceles

b)

21.1, Scalene

c)

24.3, Scalene

d)

24.3, Equilateral

33.

If a triangle with vertices of (-3,0), (0,3), (3,0), classify it by its sides.

a)

Isosceles

b)

Scalene

c)

Equilateral

d)

Obtuse

34.

If AB = 2x+3, BC = 3x-5, and AC = 38, what is the value of x ?

a)

11

b)

12

c)

8

35.

If DF=9x-39, find EF.

a)

16

b)

58

c)

116

d)

23

36.

a)

WX

b)

XY

c)

YW

d)

None

37.

a)

VW

b)

WU

c)

UV

d)

None

38.

a)

RQ

b)

QS

c)

SR

d)

None

39.

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.

40.

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

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.

41.

It means that the two statements have the same truth values for every possible interpretation.

a)

Logically Equal Statements

b)

Logically Equivalent Statements

c)

Logical Equal Statements

d)

Logical Equivalent Statements

42.

Which statement is logically equivalent to the conditional statement?

a)

converse

b)

inverse

c)

contrapositive

d)

reverse

43.

Which two statements should both be true to have a biconditional statement?

a)

conditional and converse

b)

conditional and inverse

c)

conditional and contrapositive

d)

converse and inverse

44.

Find x

a)

90

b)

45

c)

22

d)

35

45.

Find the value of the base angle.

a)

30

b)

120

c)

60

d)

180

46.

Find the distance between (-12, 1) and (12, -1).

a)

24.05

b)

24.06

c)

24.07

d)

24.08

47.

Find the distance between (-5, -8) and (-1, -16).

a)

8.9

b)

9.8

c)

10.3

d)

11

48.

Level 3

Given the line 2x-3y=9, write the equation of a line parallel to it that passes through the point (4, -1)

a)

y = 2/3x - 3

b)

y = 2/3x - 11/3

c)

y = 2/3x - 4

d)

y = 2/3x - 5/3

49.

Which of the following lines is PARALLEL to the graph of y = -6x + 3 and goes through the point (-1,4)?

a)

y=1/6x +25/6

b)

y = 1/6x + 4

c)

y = -6x - 2

d)

y = -6x + 4

50.

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.

51.

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.

52.

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

53.

Find the measure of one interior angle in each regular polygon. Round your answer to the

nearest tenth if necessary.

a)

A

b)

B

c)

C

d)

D

54.

For any rhombus JKLM, decide whether the statement is true Always, Sometimes, or Never.
$\overline{JL}\cong\overline{KM}$

a)

Always

b)

Sometimes

c)

Never

55.

For any rectangle wxyz, decide whether the statement is true Always, Sometimes, or Never.
$\overline{wy}\cong\overline{xz}$

a)

Always

b)

Sometimes

c)

Never

56.

For any rectangle wxyz, decide whether the statement is true Always, Sometimes, or Never.
$\overline{wy\ }\perp\overline{\ xz}$

a)

Always

b)

Sometimes

c)

Never

57.

Select each quadrilateral for which the statement is true.

Diagonals are perpendicular

a)

trapezoid

b)

Parallelogram

c)

Rectangle

d)

Rhombus

e)

Square

58.

Select each quadrilateral for which the statement is true.

Diagonals bisect each other

a)

trapezoid

b)

Parallelogram

c)

Rectangle

d)

Rhombus

e)

Square

59.

What is the sum of the exterior angles?

a)

90 degrees

b)

180 degrees

c)

540 degrees

d)

360 degrees

60.

Given a regular polygon. Determine is the value of x ?

a)

x =72 degrees

b)

x = 45 degrees

c)

x = 360 degrees

d)

x = 540 degrees

61.

Given a regular polygon. Determine the value of x.

a)

40 degrees

b)

180 degrees

c)

60 degrees

d)

390 degrees

62.

Find the length of PO.

a)

32

b)

35

c)

26

d)

29

63.

Given: AG = 10, find the length of BG.

a)

10

b)

20

c)

5

d)

30

64.

Adam drafts his favorite modular home on a scale drawing. The drawing scale is 2 inches for each foot. If the drawing is

60 inches long, how long is the actual modular home?

a)

120 in

b)

120 ft

c)

30 in

d)

30 ft

65.

A map has a scale of 2 cm for every 25 miles. The distance on the map between Griffin Park and the San Diego Zoo is 10 cm. How far is the actual distance?

a)

125 mi

b)

250 mi

c)

20 mi

d)

5 mi

66.

Solve for x. Round to the nearest tenth.

a)

7.5

b)

34.1

c)

14.1

67.

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

68.

Find x.

a)

42.9

b)

21

c)

33.3

d)

21.9

69.

Find x.

a)

41.8

b)

48.2

c)

33.7

70.

What is the area of the shaded region?

a)

20 $cm^2$

b)

4 $cm^2$

c)

30 $cm^2$

d)

24 $cm^2$

71.

What is the area of the shaded region?

a)

14 m²

b)

120 m²

c)

106 m²

d)

134 m²

72.

Find the area of the composite figure

a)

40 $ft^2$

b)

9 $ft^2$

c)

49 $ft^2$

d)

61 $ft^2$

73.

What if the value of x?

a)

16

b)

12

c)

4

d)

64

74.

What is the value of f?

a)

20

b)

15

c)

25

d)

50

75.

Find the value of x.

a)

15√5

b)

5√5

c)

5√3

d)

3√5

76.

Find the value of y.

a)

5

b)

10√30

c)

√300

d)

10√3

77.

Find the area of the sector, rounding your answer to 1d.p.

a)

67.1cm²

b)

67.0cm²

c)

16.8cm²

d)

134.0cm²

78.

Find the area of the shaded sector of circle O. The radius is 6 inches and the central angle is 100°. Express answer to the nearest tenth of a square inch.

a)

9.2 sq. in.

b)

10.5 sq. in.

c)

31.4 sq. in.

d)

38.2 sq. in.

79.

FIND THE SECTOR AREA OUTLINED IN BOLD

a)

A

b)

B

c)

C

d)

D

80.

Find the indicated measure. Enter your answer as a number only.

(a)

81.

Find the indicated measure. Enter your answer as a number only.

(a)

82.

$\angle J=$

a)

$88\degree$

b)

$45\degree$

c)

$135\degree$

d)

$108\degree$

83.

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

a)

72º

b)

45º

c)

36º

d)

27º

84.

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

a)

190º

b)

130º

c)

120º

d)

70º

85.

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

a)

136º

b)

70º

c)

68º

d)

66º

86.

Find the value of x.

a)

15

b)

13

c)

3

d)

6

87.

Find the value of x. Round to the nearest whole number if necessary.

(a)

88.

Solve for the indicated Segment

(a)

89.

There are 6 red marbles, 5 green marbles, and 4 yellow marbles in a bag. If Joe picks 2 marbles one after the other without replacement, then what is the probability that both are red in color?

a)

2/5

b)

1/21

c)

4/25

d)

1/7

90.

There are 5 red roses, 3 yellow roses, and 8 white roses in a tray. If Stephanie picked 2 roses one after the other without replacing, then what is the probability of picking a white rose first and a red rose next?

a)

1/6

b)

5/6

c)

1/3

d)

2/3

91.

A basket contains 5 purple pencils and 9 brown pencils. If two pencils are picked at random one after the other without replacement, then what is the probability that both the pencils are purple?

a)

9/182

b)

5/182

c)

2/91

d)

10/91

92.

Solve for x.

a)

7.94

b)

8

c)

10.58

d)

112

93.

a)

A

b)

B

c)

C

d)

D

94.

a)

A

b)

B

c)

C

d)

D

95.

a)

5

b)

7

c)

6

d)

8

96.

Find the value of X. Round to the nearest tenth.

a)

5.5

b)

6.1

c)

5.7

d)

5.2

97.

a)

612in²

b)

558in²

c)

672in²

98.

Find the Total Surface area of the cylinder.

a)

62.8m

b)

477.28 cm²

c)

235.5 cm³

d)

942 cm²

99.

Find the probability that a randomly chosen point in the figure lies in the shaded region.

a)

52.3%

b)

51.4%

c)

47.6%

d)

45.7%

100.

A point is randomly chosen on . Find the probability that a point chosen at random will NOT be in the triangle.
(Round to the nearest hundredth)

a)

0.84

b)

0.16

c)

0.30

d)

0.15

101.

Which similarity theorem, if any, proves that these triangles are similar?

a)

SSS

b)

SAS

c)

AA

d)

None, the triangles are not similar

102.

What is the "statement" for step 2 of the proof?

a)

AD=AD

b)

AD=DA

c)

HD=DN

d)

HA = AN

103.

What is statement #2?

a)

∠ABC≅∠EDC

b)

∠BCA≅∠DCE

c)

BC≅CD

d)

∠E≅∠A

104.

At point on the ground 50 feet from the front of a tree, the angle of elevation to the top of the tree is 48^𝑜 . Find the height of the tree.

Which of the following is the correct diagram for the problem?

a)

b)

c)

d)

105.

A ladder is leaning against a wall. The foot of the ladder is 6.5 feet from the wall. The ladder makes an angle of $74^o$ with the level ground. How high on the wall does the ladder reach?

a)

20.15 ft

b)

22.67 feet

c)

25.63 feet

d)

15.36 feet

106.

Find the probability that a point K selected randomly on AE is not on AD. Express your answer as a simplified fraction.

(a)

107.

A point is randomly chosen on . Find the probability of picking a point NOT on $\overline{BC}$

a)

$\frac{1}{3}$

b)

$\frac{3}{4}$

c)

$\frac{2}{3}$

d)

$\frac{7}{12}$

108.

Find the lateral area and surface area of each figure. Round your answers to the nearest tenth, if necessary.

a)

183.0 cm²; 233.2 cm²

b)

188 cm²; 259 cm²

c)

83.7 cm²; 93.2 cm²

d)

190 cm²; 240 cm²

109.

a)

103.67 yd²

b)

263.89 yd²

c)

75.4 yd²

d)

150.8 yd²

110.

The 12 school teams are participating in a quiz contest, then the number of ways the first , second and third position may be won is ________.

a)

1, 230

b)

1, 320

c)

3, 210

d)

none of these

111.

Find the coordinates of point B.

The coordinates of point A are given in the diagram.

a)

(0,0,5)

b)

(0,7,0)

c)

(8,0,0)

d)

(8,7,0)

112.

Find the coordinates of point B.

The coordinates of point A are given in the diagram.

a)

(0,0,4)

b)

(9,8,0)

c)

(9,0,0)

d)

(0,8,4)

113.

Find the area of the regular heptagon.

a)

700.56

b)

734.12

c)

745.83

d)

802.15

114.

Find the area of the regular octagon.

a)

543

b)

612

c)

696

d)

793

115.

Write the equation of a circle with center (7, 0) with radius 3.

a)

(x - 7)² + y² = 9

b)

x² + (y -7)² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

116.

The diameter of a circle has length 12. The center is at (-5, 2). Give the equation of the circle.

a)

(x - 2)²+ (y + 5)²= 36

b)

(x - 5)² + (y + 2)² = 6

c)

(x + 5)²+ (y - 2)²= 36

d)

(x + 2)²+ (y - 5)²= 6

117.

Two spheres have a scale factor ratio of 1:3. The smaller sphere has a surface area of 16 ft²_. Find the surface area of the larger sphere.

a)

48 ft²

b)

144 ft²

c)

432 ft²

d)

32 ft²

118.

The ratio of the volume of two spheres is 8:27. What is the ratio of their radii?

a)

2:3

b)

4:9

c)

3:4

d)

64:729

119.

The height (but not the base) of a triangle is doubled. Describe the effect on the area.

a)

The area is doubled

b)

The area is quadrupled

c)

The area is halved

120.

Describe the transformation:

(x, y) -> (x-2, y+7)

a)

Translation 2 units to the left & 7 units up

b)

Translation 2 units to the left & 7 units down

c)

Translation 2 units to the right & 7 units up

d)

Translation 2 units to the right & 7 units down

121.

Describe the transformation:

(x, y) -> (y, -x)

a)

reflection across the x-axis

b)

reflection across the y-axis

c)

rotation 90 degrees clockwise

d)

rotation 90 degrees counterclockwise

122.

Describe the transformation:

(x, y) -> (-y, x)

a)

reflection across the x-axis

b)

reflection across the y-axis

c)

rotation 90 degrees clockwise

d)

rotation 90 degrees counterclockwise

123.

Describe the transformation:

(x, y) -> (-x, y)

a)

reflection across the x-axis

b)

reflection across the y-axis

c)

rotation 90 degrees clockwise

d)

rotation 90 degrees counterclockwise

124.

The ratio of the measures of the angles of a triangle is 6:2:7. Find the measure of the largest angle.

a)

15

b)

30

c)

84

d)

90

125.

The ratio of the measures of the angles of a triangle is 17:3:10. Find the measure of the medium angle.

a)

6º

b)

18º

c)

60º

d)

102º

126.

cos(5π/3)

a)

-√2/2

b)

-1/2

c)

1/2

d)

√3/2

127.

tan(3π/4)

a)

√2/2

b)

-√2/2

c)

√3/2

d)

-1

128.

tan(300^o)

a)

-√3 /3

b)

½

c)

2√3 /3

d)

-√3

129.

Find XZ

a)

16.004 meters

b)

544.165 meters

c)

34.7 meters

d)

1204.165 meters

130.

Use Law of Cosines to find angle T

a)

62.2°

b)

53.1°

c)

59.5°

d)

64.7°

131.

What is the measure of angle A?

a)

58 degrees

b)

61 degrees

c)

78 degrees

d)

74 degrees

132.

Find AC

a)

12

b)

10

c)

23

d)

14

133.

Find c

a)

10

b)

8

c)

6.1

d)

4.9

134.

What are the coordinates of point A' , the image of point A(-4, 1) after the composite transformation R₉₀ (rotation 90 ccw about origin) then r_{y= -x} (reflection over diagonal line y= -x)?

a)

(-1, -4)

b)

(-4, -1)

c)

(1, 4)

d)

(4, 1)

135.

Under what composition of transformations does triangle ABC map onto triangle A''B''C''

a)

Reflection over x-axis, then Rotation of 90 Degrees

b)

Rotation of -90 Degrees, then Reflection over y-axis

c)

Reflection over y-axis, then Rotation of -90 Degrees

d)

Rotation of 90 Degrees, then Reflection over x-axis

136.

Find the new coordinates of Triangle MRV M(2,-1) R(2,-5) V(4,-5) when rotated $90\degree$ clockwise and reflected over the y-axis.

a)

M'(-1,2) R'(-5,-2) V'(-5,-4)

b)

M''(1,-2) R''(5,-2) V''(5,-4)

c)

M''(-2,1) R"(-2,5) V"(-4,5)

d)

M(-1,2) R(-5,2) V(-5,4)

137.

Find the missing length.

a)

25

b)

15

c)

6

d)

16

138.

Solve for x.

a)

7

b)

3

c)

9

d)

10

139.

An airplane is traveling at 230 mph on a bearing of S 75 W. Wind is blowing at 85 mph on a bearing of S 40 E. What is the ground speed and actual bearing of the plane?

a)

$132.2\ mph,\ 43.5\degree$

b)

$208.8\ mph\ ,\ 36.6\degree$

c)

$202.6\ mph\ ,\ 45.8\degree$

d)

$316.1\ mph\ ,\ 34.4\degree$

140.

An airplane flies due north at 150 km/h with respect to the air. There is a wind blowing at 75 km/h due east. What are the plane's speed with respect to the ground?

a)

167.7 km/h at 26.6 degrees north of east

b)

225 km/h at 26.6 degrees east of north

c)

167.7 km/h at 63.4 degrees north of east

d)

129.9 km/h at 63.4 degrees north of east

e)

129.9 km/h at 26.6 degrees east of north

141.

Find the magnitude of the vector <10, -8>

a)

2

b)

12.81

c)

6

d)

18

142.

Determine the direction and magnitude of the vector 〈7,18〉

a)

Direction 21.3°
Magnitude 19.3

b)

Direction 68.7°
Magnitude 19.3

c)

Direction 21.3°
Magnitude 373

d)

Direction 68.7°
Magnitude 373

143.

What is the order and angle of rotation of the flag?

a)

Order 2, 180 degrees

b)

Order 4, 90 degrees

c)

Order 3, 120 degrees

d)

Order 1, 360 degrees

Review Geometry CBE

Total questions: 143

Worksheet time: 6hrs 45mins

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