Free Printable Geometry AIR Review

1.

Do the following side lengths form a triangle?
2 inches, 2 inches, 4 inches

a)

Yes

b)

No

2.

If the longest side of the triangle was 10. Then the two shorter sides must have a sum that is ....?

a)

any length

b)

equal to 10

c)

greater than 10

d)

less than 10

3.

which of the following pairs of angles have the same measure?

a)

angle 1 and angle 7

b)

angle 2 and angle 3

c)

angle 3 and angle 6

d)

angle 4 and angle 5

4.

What it the measurement for angle 1?

a)

140^o

b)

180^o

c)

40^o

d)

160^o

5.

Determine how to translate triangle ABC to triangle A'B'C'.

a)

right two, down five

b)

right two, down 9

c)

left two, up 9

d)

left two, down 5

6.

Determine where X' would be if you translated X 3 units to the left and 9 units down.

a)

(-4, 4)

b)

(-10, 2)

c)

(-4, -5)

d)

(-1, 5)

7.

What does a translation do to an image?

a)

Turns it 90* clockwise

b)

Mirrors it

c)

Shrinks it

d)

Slides it

8.

Which answer shows a reflection across the y-axis?

a)

a

b)

b

c)

c

d)

d

9.

Find K' if the figure is reflected across the x-axis

a)

(4, 1))

b)

(-1, -4)

c)

(1, -4)

d)

(1, 4)

10.

A turn is also called a ___________.

a)

Translation

b)

Reflection

c)

Rotation

d)

Transformation

11.

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

12.

Identify the transformation from C to D.

a)

90^o Clockwise Rotation

b)

180^o Rotation

c)

270^o Clockwise Rotation

d)

360^o Rotation

13.

Rotating a pre-image _____degrees will place it back to its original position.

a)

180

b)

90

c)

270

d)

360

14.

The point Z(4, -2) is rotated 180 degrees about the origin. What is the image of Z?

a)

Z'(2, 4)

b)

Z'(-4, 2)

c)

Z'(-2, -4)

d)

Z'(-4, -2)

15.

Is the picture being reflected in the y-axis or x-axis?

a)

y-axis

b)

x-axis

16.

Translate the point A (-3, 4) right 5 and up 1

a)

(-2, 9)

b)

(-8, 5)

c)

(8, 3)

d)

(2, 5)

17.

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

a)

(x+8, y+4)

b)

(x-8, y-4)

c)

(x+4, y+8)

d)

(x-4, y-8)

18.

Describe the transformation shown in the graph.

a)

Reflect over x-axis

b)

Reflect over y-axis

c)

Rotate 270 degrees CCW

d)

Rotate 90 degress CCW

19.

Name the image of C(6, -4) under a rotation 90 degrees counterclockwise about the origin.

a)

C'(4, 6)

b)

C'(-4, -6)

c)

C'(6, 4)

d)

C'(-6, -4)

20.

A dilation produces a similar figure

a)

True

b)

False

21.

When the scale factor of a dilation is less than one, the dilation is a reduction (gets smaller).

a)

True

b)

False

22.

An image is dilated at a scale factor of 1.5. This means the dilation is an enlargement and the dilated image will be bigger.

a)

True

b)

False

23.

Choose the correct scale factor:

a)

2

b)

3

c)

1/3

d)

1/2

24.

Dilate Point B by a scale factor of 3:

a)

(12,0)

b)

(12,12)

c)

(4,3)

d)

(0,12)

25.

Does the image show a dilation?

a)

Yes

b)

No

26.

What is the justification (reason)?

a)

reflexive property

b)

definition of segment bisect

c)

definition of a midpoint

d)

substitution property

27.

What is the justification (reason)?

a)

Reflexive Property

b)

Symmetric Property

c)

Transitive Property

d)

Substitution

28.

Which of the following is NOT a triangle congruence criteria?

a)

SAS

b)

AAS

c)

SSA

d)

ASA

29.

What does CPCTC stand for?

a)

Corresponding Parts of Congruent Triangles are Congruent

b)

Congruent Parts of Congruent Triangles are Corresponding

c)

Colorful Pieces of Corresponding Triangles are Congruent

d)

Congruent Pieces of Congruent Triangles are Congruent

30.

A parallelogram is a rectangle when the diagonals ...

a)

are perpendicular.

b)

bisect each other.

c)

are congruent.

d)

are parallel.

31.

When using hypotenuse leg (HL) in a proof, you must first state ...

a)

CPCTC.

b)

there are right triangles.

c)

that vertical angles are congruent.

d)

the reflexive property.

32.

What triangle congruence criteria is shown in the given diagram?

a)

AAS

b)

ASA

c)

SSA

d)

SAS

33.

What triangle congruence criteria is shown in the given diagram?

a)

SSS

b)

SAS

c)

ASA

d)

AAS

34.

A triangle with two congruent sides and two congruent angles (base angles) is called ...

a)

scalene

b)

equilateral

c)

isosceles

d)

obtuse

35.

A centroid is formed by the point of concurrency of three __________ of a triangle.

a)

altitudes

b)

medians

c)

perpendicular bisectors

d)

angle bisectors

36.

A median of a triangle connects the ___________ of a side to the opposite vertex.

a)

midpoint

b)

right angle

c)

end point

d)

angle

37.

A centroid breaks the median of a triangle into a ________ ratio.

a)

1:1

b)

2:1

c)

3:1

d)

4:1

38.

If point B is the centroid and BC = 12, what is the length of AB?

a)

12

b)

8

c)

6

d)

4

39.

What is the missing piece of information required to prove these triangles congruent?

a)

QY ≅ QY

b)

NY ≅ PY

c)

∠N ≅ ∠P

d)

QY is the perpendicular bisector

40.

Which quadrilateral has diagonals that are always perpendicular bisectors of each other?

a)

trapezoid

b)

parallelogram

c)

rectangle

d)

square

41.

The orthocenter is the point of concurrency for three ...

a)

perpendicular bisectors

b)

angle bisectors

c)

medians

d)

altitudes

42.

Name the property of equality or congruence that justifies going from the first statement to the second statement.

a)

Reflexive Property of Congruence

b)

Symmetric Property of Congruence

c)

Distributive Property

d)

Transitive Property of Congruence

43.

What is the REASON for Statement #3?

a)

Given

b)

Definition of Complementary Angles

c)

Substitution Property

d)

Reflexive Property of Congruence

44.

What is the REASON for Statement #5?

a)

Addition Property of Equality

b)

Subtraction Property of Equality

c)

Multiplication Property of Equality

d)

Division Property of Equality

45.

What is the REASON for Statement #6?

a)

Addition Property of Equality

b)

Subtraction Property of Equality

c)

Multiplication Property of Equality

d)

Division Property of Equality

46.

Supply the second reason.

a)

Linear Pair Postulate

b)

Alternate Interior Angles Theorem

c)

Vertical Angles Theorem

d)

Corresponding Angles Postulate

47.

Supply the third reason.

a)

Vertical Angle Theorem

b)

Corresponding Angles Postulate

c)

Alternate Interior Angles Postulate

d)

Same Side Interior Angles Theorem

48.

Which property justifies the next step?

a)

Definition of linear pair

b)

Definition of supplementary angles

c)

Congruent supplements thm

d)

Linear pair postulate

49.

If angles are supplementary to the same angle then those two angles are congruent

a)

Congruent Supplements

b)

Multiplication Property

50.

Find the measure of angle 1.

a)

28^o

b)

136^o

c)

44^o

d)

6^o

51.

Solve for y.

a)

y = 20

b)

y = 120

c)

y = 60

d)

y = 10

52.

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

a)

median

b)

altitude

c)

midsegment

d)

sangle bisector

53.

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

a)

midsegment

b)

perpendicular bisector

c)

altitude

d)

midsegment

54.

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

a)

angle bisector

b)

midsegment

c)

altitude

d)

median

55.

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

a)

altitude

b)

perpendicular bisector

c)

midsegment

d)

angle bisector

56.

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

a)

angle bisector

b)

perpendicular bisector

c)

median

d)

midsegment

57.

Find the missing angle TSR.

a)

A

b)

B

c)

C

d)

D

58.

Name the smallest angle in this triangle.

a)

∠A

b)

∠B

c)

∠C

59.

Find the value of x by using the exterior angle theorem.

a)

A

b)

B

c)

C

d)

D

60.

a)

AB>AC

b)

AB<AC

c)

AB=AC

d)

No conclusion can be made

61.

a)

Dave

b)

Ellen

62.

Order the sides from greatest to least

a)

a , b , c

b)

b , c , a

c)

c , b , a

d)

a , c , b

63.

Which of the following statements must be true?

a)

RS > XY

b)

RS < XY

c)

ST < XZ

d)

$\angle T\ >\angle Z$

64.

Select all that are TRUE.

a)

AB > AE

b)

BE > CE

c)

BE > CD

d)

CD < DE

e)

CE > BC

65.

Level 2

Solve for the value of y

a)

13

b)

5

c)

23

d)

10

66.

Level 3

Find the length of the missing side.

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

67.

_{^{Find the missing side}}

a)

9

b)

41

c)

6.4

d)

3

68.

Does the set of numbers represent a right triangle?

20, 25, 15

a)

Yes

b)

No

69.

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

a)

111.8 yards

b)

115 yards

c)

127.3 yards

d)

119 yards

70.

Tanya runs diagonally across a rectangular field that has a length of 40 yards and a width of 30 yards. What is the length of the diagonal, in yards, that Tanya runs?

a)

26.5 yards

b)

10 yards

c)

50 yards

d)

46.7 yards

71.

Find x.

a)

30°

b)

60°

c)

90°

d)

180°

72.

Find x.

a)

10

b)

√3

c)

5

d)

10√3

73.

Find x.

a)

4

b)

2

c)

√3

d)

2√2

74.

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

a)

Multiply 4 by 2

b)

Multiply 4 by √3

c)

Multiply 4 by √2

d)

Divide 4 by √3

75.

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

a)

5

b)

5√2

c)

10

d)

5√3

76.

A triangle has the following side lengths:
AB = 12 units
BC = 10 units
AC = 16 units
What type of triangle does this make?

a)

Acute

b)

Obtuse

c)

Right

77.

If the sum of the interior angles of a polygon equals 900°, how many sides does the polygon have?

a)

7

b)

9

c)

10

d)

12

78.

What is the value of x?

a)

26.25

b)

38.75

c)

24

d)

25.125

79.

An exterior angle of a regular polygon
measures 36°. How many sides does
the polygon have?

a)

10

b)

5

c)

14

d)

9

80.

The measurement of the sum an interior
angle of a regular nonagon is 1080°

a)

True

b)

False

81.

Find the value of x

a)

141

b)

150

c)

135

d)

163

82.

Find the measureof the sum of the exterior angles in a hexagon

a)

360

b)

180

c)

720

d)

540

83.

Find the value of one angle measurein a pentagon

a)

108

b)

60

c)

120

d)

135

84.

An exterior angle measure of a regular polygon is 22.5^o. How many sides does the polygon have?

a)

18

b)

16

c)

20

d)

14

85.

Which formula is used to find the number of diagonals in a polygon?

a)

180

b)

360

c)

(n-2)180

d)

n(n-3)/2

86.

Which polygon has 14 diagonals?

a)

Hexagon

b)

Octagon

c)

Nonagon

d)

Heptagon

87.

Find the measure of one interior angle in a regular polygon if it has 35 diagonals.

a)

10

b)

35

c)

40

d)

144

88.

Check all that are true of a PARALLELOGRAM

a)

opposite sides are parallel

b)

opposite sides are congruent

c)

all sides are congruent

d)

opposite angles are congruent

e)

all angles are congruent

89.

Check all that are true of a RECTANGLE

a)

opposite sides are parallel

b)

opposite sides are congruent

c)

all sides are congruent

d)

opposite angles are congruent

e)

all angles are congruent

90.

Check all that are true of a RHOMBUS

a)

opposite sides are parallel

b)

opposite sides are congruent

c)

all sides are congruent

d)

opposite angles are congruent

e)

all angles are congruent

91.

Check all that are true of a SQUARE

a)

opposite sides are parallel

b)

opposite sides are congruent

c)

all sides are congruent

d)

opposite angles are congruent

e)

all angles are congruent

92.

TRUE or FALSE: All quadrilaterals are parallelograms.

a)

True

b)

False

93.

TRUE or FALSE: A parallelogram with a right angle is a square.

a)

True

b)

False

94.

TRUE or FALSE: All rhombuses are squares.

a)

True

b)

False

95.

Given Rhombus TUVW. Find m∠2.

a)

62

b)

28

c)

90

d)

78

96.

Find the measure of angle 1

a)

54

b)

108

c)

72

d)

36

97.

If the figure is a rectangle, the value of x is...

a)

2

b)

12

c)

13

d)

28

98.

Find the missing angle of the trapezoid.

a)

65

b)

115

c)

180

d)

None of these

99.

In a parallelogram, consecutive angles are __________.

a)

congruent

b)

supplementary

c)

corresponding

d)

parallel

100.

Find the measure of ∠K:

a)

114°

b)

124°

c)

77°

d)

66°

101.

Solve for x. Round to the nearest tenth.

a)

7.5

b)

34.1

c)

14.1

102.

a)

18.9

b)

19.5

c)

47

d)

27.5

103.

What is the length of side x?

a)

6.57 cm

b)

7 cm

c)

7.44 cm

d)

26.33 cm

104.

Find h₁

a)

6.69 ft

b)

11.11 ft

c)

9.00 ft

d)

7.43 ft

105.

Solve for the missing angle

a)

50

b)

0.053

c)

36.9

d)

95

106.

Find the measure of the missing angle.

a)

64^o

b)

26^o

c)

61^o

d)

.008^o

107.

Which scenario describes the picture shown?

a)

A 5 foot ramp is 8 feet away from a building. What is the angle that the ramp makes with the ground?

b)

A 5 foot ramp leans against an 8 foot structure. What is the angle that the ramp makes with the ground?

c)

An 8 foot ramp leans
against a building 5 feet away. What angle does the ramp make with the ground?

d)

A 5 foot man is 8 feet away from a building. What is the angle of elevation?

108.

Round your answer to the nearest tenth.

a)

1747.5 ft.

b)

1319.3 ft.

c)

1428.2 ft.

d)

2747.5 ft.

109.

A 10 ft. tree creates a shadow that is 15 ft. long. Find the angle of elevation of the sun.

a)

34 degrees

b)

56 degrees

c)

72 degrees

d)

15 degrees

110.

1

a)

A

b)

B

c)

C

d)

D

111.

Find angle Z

a)

20.15°

b)

71.23°

c)

51.06°

d)

57.71°

112.

Find the Area of this triangle

a)

19.8 km²

b)

37.8 km²

c)

18.9 km²

d)

35 km²

113.

What is the area of the composite figure?

a)

40 sq cm

b)

65 sq cm

c)

52.5 sq cm

d)

25 sq cm

114.

Find the area of the polygon.

a)

6.25 mi²

b)

8.75 mi²

c)

7 mi²

d)

10.25 mi²

115.

Find the area of the circle. (Use $\pi$ = 3.14)

a)

$100.4\ cm^2$

b)

$50.2\ cm^2$

c)

$201\ cm^2$

d)

$25.1\ cm^2$

116.

Find the circumference of the circle. (Use $\pi$ = 3.14)

a)

201 cm

b)

100.4 cm

c)

25.1 cm

d)

50.2 cm

117.

Find the volume of the cube.

a)

$16\ in^3$

b)

$64\ in^3$

c)

$20\ in^3$

d)

$12\ in^3$

118.

Find the volume of the sphere. (Use $\pi$ = 3.14)

a)

$6104.2\ m^3$

b)

$254.3\ m^3$

c)

$3745.7\ m^3$

d)

$3052.1\ m^3$

119.

Find the Lateral surface area of the cylinder. (Use $\pi$ = 3.14)

a)

$942\ m^2$

b)

$471\ m^2$

c)

$47.1\ m^2$

d)

$1884\ m^2$

120.

Find the volume of the triangular prism.

a)

$1080\ m^3$

b)

$270\ m^3$

c)

$540\ m^3$

d)

$424.6\ m^3$

121.

Find the total surface area of the cone. (Use $\pi$ = 3.14)

a)

$602.8\ m^2$

b)

$301.4\ m^2$

c)

$150.7\ m^2$

d)

$1088.2\ m^2$

122.

Find the total surface area of the cube.

a)

$96\ in^2$

b)

$64\ in^2$

c)

$16\ in^2$

d)

$56\ in^2$

123.

2. The figure shows a circle inside a triangle. Which equation could be used to find the area of the shaded region?

a)

A = ½bh - 2πr

b)

A = πr² - ½bh

c)

A = ½bh - πd

d)

A = ½bh - πr²

124.

What is the area of the shaded region?

a)

14 m²

b)

120 m²

c)

106 m²

d)

134 m²

125.

a)

122.46 mi²

b)

122. 45 mi²

c)

175.84 mi²

d)

175.85 mi²

126.

Find the arc length. Leave your answer in terms of π.

a)

7/4π

b)

7/2π

c)

1/8π

d)

45π

127.

Find the length of the bold arc.Leave pi in your answer.

a)

5688π ft

b)

15.8π ft

c)

150.4π ft

d)

54,150 ft

128.

Find the area of each sector.

a)

52.4 in²

b)

18,864 in²

c)

60 in2

d)

10.47 in

129.

Find the area of the shaded sector of the circle.

a)

b)

c)

d)

130.

Lines AO and BO are tangent. What is the measure of BO?

a)

20

b)

15

c)

10

d)

5

131.

find the measure of angle a

a)

30

b)

21

c)

60

d)

120

132.

find the measure of x

a)

38

b)

21

c)

27

d)

96

133.

Find the measure of angle BDC.

a)

35

b)

40

c)

75

d)

110

134.

Find the measure of angle EFH.

a)

61

b)

65

c)

114

d)

130

135.

Is line AB tangent to the circle?

a)

YES

b)

NO
NO

c)

Can't Tell
Can't Tell

136.

Find the perimeter

a)

48.8

b)

47.4

c)

39.8

d)

36.4

137.

What can you conclude from the picture?

a)

m is parallel to circle C

b)

m is skew to circle C

c)

m bisects circle C

d)

m is tangent to circle C

138.

What can you conclude?

a)

AB and AC are not congruent.

b)

AB= half of AC

c)

AC = half of AB

d)

AB=AC

139.

Find the measure of angle ABD.

a)

14

b)

51

c)

37

d)

65

Geometry AIR Review

Total questions: 139

Worksheet time: 7hrs 16mins

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