Free Printable Question Bank for Grade 9 Mathematics

1.

Determine if the change from the smaller triangle is proportinal and describe how the changes affect its perimeter and area.

4 lines

2.

The circumference of the following circle is 12π units.
What is the area of the shaded region?

a)

36π square units

b)

12π square units

c)

8π square units

d)

32π square units

3.

A regular pentagon has an apothem of 3 yards. What is the area of the regular pentagon in square centimeters? Round your answer to the nearest tenth.

a)

41 yd²

b)

33 yd²

c)

132.0 yd²

d)

4.1 yd²

4.

Given the following triangle, find the slope of the altitude that connects from Point B to side AC.

a)

m=1/2

b)

m=2

c)

m=-1/2

d)

m=-2

5.

Find the area of the shaded region:

a)

66x³ + 12x²

b)

80x²- 24x

c)

66x³ + 40x² + 24x

d)

66x³ + 92x² -24x

6.

An unknown quadrilateral has these points:

P(0,3) ,Q(5,7), R(6,1), S(1,-3)

What is true about PQ and RS? (Select all that apply)

a)

They are parallel

b)

They are congruent

c)

They are perpendicular

d)

They are skew

7.

Consider a quadrilateral and its diagonals. Which conjecture would best describe a quadrilateral whose diagonals divide it into four congruent isosceles right triangles.

a)

Rectangle

b)

Parallelogram

c)

Trapezoid

d)

Square

e)

Rhombus

8.

Find the area of the shaded region. Only type the number part of the answer.

(a)

9.

a)

A

b)

B

c)

C

d)

D

10.

Given that the smaller triangle has an area of 22 square units. Find the area of the bigger triangle.

a)

66 square units

b)

88 square units

c)

264 square units

d)

154 square units

11.

Three vertices of parallelogram ACBD are shown on the coordinate plane. Which of the following coordinate pairs could be the fourth vertex, D of the parallelogram?

a)

(-1, 3)

b)

(2,-3)

c)

(-1,-3)

d)

(5,3)

12.

In the following circle, the length of the major arc is (49/2)π centimeters and its measure is 315 degrees. What is the length of the radius of the circle.

a)

14 cm

b)

196 cm

c)

98 cm

d)

24.5 cm

13.

The figure is a rhombus.

Solve for x.

a)

1

b)

11

c)

7

d)

6

14.

For parallelogram KLMN, solve for x and y. Note: LJ=3y-7 and NJ=y+15.

a)

x = 3, y = 11

b)

x = 4, y = 11

c)

x = 11, y = 4

d)

x = 9, y = 7

15.

Solve for x.

a)

x = 16

b)

x = 13

c)

x = 7

d)

x = 10

16.

Find the measure of angle 2

a)

54

b)

108

c)

72

d)

36

17.

Given the rhombus, find the measure of angle 1

a)

50

b)

25

c)

90

d)

65

18.

Find the measure of n:

a)

117

b)

63

c)

25

d)

39

19.

Find the median of the following trapezoid.

a)

10.5

b)

4.5

c)

12

d)

10

20.

ABCD is a parallelogram. Find the value of x. (Remember: Consecutive angles are supplementary.)

a)

12

b)

50

c)

13

d)

14

21.

Solve for x in the rectangle.

a)

25

b)

20

c)

30

d)

25/3

22.

If WR= 27, what is WX? (Hint: Use Pythagorean Theorem)

a)

38.2

b)

27

c)

13.5

d)

1458

23.

Kate built a garden box with 4 sides. It has two sets of opposite parallel sides. Which of the following shapes could her garden NOT be? (select all that apply)

a)

rectangle

b)

trapezoid

c)

square

d)

parallelogram

e)

kite

24.

What is False about the quadrilateral?

a)

It has 2 sets of opposite sides congruent

b)

Consecutive sides are perpendicular

c)

It has opposite sides parallel

d)

It is a parallelogram

25.

Find the length of arc WY.

a)

$\frac{25}{6}\pi$ m

b)

$\frac{25}{3}\pi$ m

c)

$\frac{65}{6}\pi$ m

d)

$\frac{65}{3}\pi$ m

26.

Given that m∠AOB = 13π/18 and the radius is 8 cm, what is the length of arc AB?

a)

13π/8 cm

b)

52π/9 cm

c)

π/9 cm

d)

9π/52

27.

An unknown quadrilateral has these points:

A(0,-3)

B(6,-3)

C(9,1)

D(3,1)

Based on your discoveries about the lengths of the sides, can this shape be a square?

a)

Yes

b)

No

28.

Find the area of the sector with the central angle of 60degrees. Approximate using the pi symbol in the calculator.

a)

52.4 in²

b)

18,864 in²

c)

60 in2

d)

10.47 in

29.

Find the area of the shaded sector of the circle.

a)

b)

c)

d)

30.

Find the sector area with the given central angle. Leave in terms of Pi.

a)

$114\pi$

b)

$147\pi$

c)

$234\pi$

d)

$125\pi$

31.

Find the EXACT area of the sector.

a)

$\frac{8\pi}{3}ft^2$

b)

$\frac{35\pi}{3}\ ft^2$

c)

$\frac{39\pi}{4}ft^2$

d)

$\frac{175\pi}{3}\ ft^2$

32.

Find the area of the sector. Round your to the nearest tenth.

(a)

33.

In a circle with a diameter of 32, the area of a sector is $\frac{512\pi}{3}$ . The measure of the angle of the sector, in radians, is

a)

$\frac{\pi}{3}$

b)

$\frac{4\pi}{3}$

c)

$\frac{16\pi}{3}$

d)

$\frac{64\pi}{3}$

34.

In circle O, the length of radius is 9 centimeters and the area of sector AOB is $\frac{27\pi}{2}$ square centimeters. The measure of the central angle AOB in degrees

(a)

35.

In a circle, a 90° sector has area 64π in². What is the radius of the circle?

a)

16 in

b)

32 in

c)

64 in

d)

128 in

36.

Find the length of WU

a)

5

b)

18

c)

3

d)

11

37.

Select the correct equation to solve for x.

a)

3x + 6 = 2x + 5

b)

5x = 11

c)

6x = 30

d)

6x² = 30

38.

Solve for x. Assume that lines which appear tangent are tangent.

a)

11

b)

17

c)

18

d)

12

39.

Find CE.

a)

12

b)

16

c)

18

d)

None of these

40.

Find x.

a)

9

b)

1

c)

27

d)

None of these

41.

a)

5

b)

12

c)

24

d)

10

42.

Find the length of BC.

a)

2

b)

3

c)

9

d)

14

43.

What is the value of x?

a)

22

b)

25

c)

15

d)

20

44.

Solve for x.

a)

7.94

b)

8

c)

10.58

d)

112

45.

Solve for a.

a)

4

b)

6.93

c)

8

d)

16

46.

What is the radius?

a)

18

b)

72

c)

38

d)

14

47.

QS is a tangent to circle P. Find QS.

a)

144

b)

14

c)

12

d)

13

48.

Find x. Assume that segments that appear to be tangent are tangent.

a)

11.2

b)

18.0

c)

25.0

d)

30.0

49.

The polygon circumscribes the circle. Find the perimeter.

a)

78

b)

84

c)

72

d)

86

50.

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

a)

57

b)

137

c)

47

d)

257

51.

Find the perimeter of the quadrilateral.

a)

A

b)

B

c)

C

d)

D

52.

a)

15

b)

20

c)

14/3

d)

3/14

53.

a)

10

b)

5

c)

2

d)

12.5

54.

a)

13

b)

16

c)

12

d)

5

55.

Solve for x.

a)

14

b)

4

c)

3

d)

18

56.

Find the measure of KM.

a)

18

b)

10

c)

17

d)

21

57.

Find the length of WU

a)

5

b)

18

c)

3

d)

11

58.

a)

5

b)

32

c)

18

d)

24

59.

***Hard Question*** AC and DB are chords that intersect at point H.

What is the length of line segment DB?

a)

4

b)

8

c)

16

d)

20

60.

Solve for d.

a)

8

b)

9

c)

10

d)

12

61.

Which equation correctly reflects the information shown in the diagram?

a)

(24)(21) = (x – 5)(x – 9)

b)

(21)(x – 5) = (24)(x – 9)

c)

(21)(x – 9) = (24)(x – 5)

d)

none of these

62.

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

a)

Yes

b)

No

63.

Acute, right, or obtuse?

a)

Acute

b)

Right

c)

Obtuse

64.

Acute, right, or obtuse?

a)

Acute

b)

Right

c)

Obtuse

65.

Acute, right, or obtuse?

a)

Acute

b)

Right

c)

Obtuse

66.

Which set of side lengths does not form a right triangle?

a)

38, 80, 90

b)

16, 63, 65

c)

36, 77, 85

d)

14, 15, 29

67.

Does the set of numbers represent a Pythagorean Triple.
4, 5, 6

a)

Yes

b)

No

68.

The lengths of a triangle are given below. Is the the triangle obtuse, acute, or right?
4, 5, 6

a)

right

b)

obtuse

c)

acute

69.

Which set of side lengths form a right triangle?

a)

4, 8, 12

b)

12, 13, 20

c)

6, 8, 10

d)

8, 8, 8

70.

12, 12, 25

a)

acute

b)

right

c)

obtuse

d)

not a triangle

71.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

72.

a = 2.1, b = 7.2,
c = 7.5
Is this a right triangle?

a)

yes

b)

no

73.

State if the three side lengths form an acute, obtuse, or right triangle.

$\sqrt[]{5},\ \sqrt[]{5},\ \sqrt[]{10}$

a)

Acute Triangle

b)

Right Triangle

c)

Obtuse Triangle

d)

Not a Triangle

74.

State if the three side lengths form an acute, obtuse, or right triangle.

2.8, 19.1, 19.7

a)

Acute Triangle

b)

Right Triangle

c)

Obtuse Triangle

d)

Not a Triangle

75.

If $a^2+b^2<c^2$ then it is a __________ triangle

a)

acute

b)

right

c)

obtuse

76.

If $a^2+b^2=c^2$ then it is a __________ triangle

a)

acute

b)

right

c)

obtuse

77.

Alan made a small four-sided table for his office. The opposite sides of the table are 27 inches long and 36 inches long. If the diagonal of the table measures 40 inches, does the table have right angles at the corners? Why or why not?

a)

Yes, because it's a rectangle and rectangles have 90 degree angles in the corners

b)

Yes, because 27 and 36 are less than 40

c)

No, because 27²+36² does not equal 40²

d)

No, because 27+36 does not equal 40

78.

State if the three side lengths form an acute, obtuse, or right triangle.

$5,\ 7,\ \sqrt[]{74}$

a)

Acute Triangle

b)

Right Triangle

c)

Obtuse Triangle

d)

Not a Triangle

79.

Solve for the misssing distance

a)

18.9 meters

b)

19.5 meters

c)

47.2 meters

d)

27.5 meters

80.

Elizabeth 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

81.

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

82.

Find side AB?

a)

20 m

b)

5 m

c)

11.54 m

d)

8.66 m

83.

When the angle of elevation of the sun is 78 degrees, a statue casts a shadow that is 6m long. How far is the top of the statue to the end of its shadow?

a)

1.2 m

b)

28.9 m

c)

6.1 m

d)

28.2 m

84.

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

85.

Heather went on a hot air balloon ride for her birthday. She was on the balloon 520m from the ground. There was a building that was 450m tall. The angle of depression from the balloon down to the top of the building was measured at 10° , find the horizontal distance from the balloon to the building in meters.

a)

512 m

b)

414 m

c)

403 m

d)

397 m

86.

Kiara's yacht is anchored 90 feet offshore from the base of a lighthouse. The angle of elevation from the boat to the top of the lighthouse is 26 degrees. The distance between the yacht and the top of the lighthouse is about 100 feet.Find the height of the lighthouse.

a)

25 feet

b)

45 feet

c)

110 feet

d)

135 feet

87.

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

88.

What trigonometric ratio would be used to find the distance from the ship to the plane?

a)

sine

b)

cosine

c)

tangent

d)

inverse sine

89.

Solve for the missing angle.

a)

50

b)

0.053

c)

36.9

d)

95

90.

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How long must the ladder be?

a)

25 feet

b)

26 feet

c)

27 feet

d)

28 feet

91.

A rectangular field is 50 yards wide and 100 yards long. Patrick walks diagonally across the field. How far does he walk? Round to the nearest tenth of a yard

a)

111.8 yards

b)

115 yards

c)

127.3 yards

d)

119 yards

92.

Marcus leans a 12-ft ladder against a wall to clean a window. If the base of the ladder is 3 ft away from the wall, how high up does the ladder reach? Simplify the radical if needed

a)

$5\sqrt{5}\ \$ feet

b)

12 feet

c)

$3\sqrt{15}\$ feet

d)

10 feet

93.

A sailing ship sails 46 km North and then 74 km East. How far is the ship from its starting point to the nearest km?

a)

67 km

b)

58 km

c)

85 km

d)

87 km

94.

Find the perimeter of a triangle that has legs that are 3 cm and 4 cm.

a)

5

b)

7

c)

10

d)

12

95.

On a sunny day, Ed notices that his shadow is 30 inches long. If it is 78 inches from the top of his head to the end of the shadow, how tall is Ed?

a)

72 inches

b)

72.1 inches

c)

84 inches

d)

83.6 inches

96.

What is the altitude of an equilateral triangle with side length of 10 in? Simplify the radical

a)

10 in

b)

$5\sqrt{3}\ in$

c)

$\ 5\sqrt{2}in$

d)

$\sqrt{75}\ in$

97.

Ashley is building a garden and she wants it to be 40' long. She knows that the diagonal measure of the plot is 50'. What is the width?

a)

30 feet

b)

50 feet

c)

40 feet

d)

20 feet

98.

A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the corner diagonally across. What is this distance?

a)

210 m

b)

180 m

c)

150 m

d)

79 m

99.

The floor of a rectangular living room is 6 meters by 8 meters. What is the distance between opposite corners of the living room?

a)

3.7 meters

b)

10 meters

c)

1.4 meters

d)

100 meters

100.

What is the distance between the lighthouse and the sailboat?

a)

100yd

b)

30yd

c)

900yd

d)

300yd

101.

A 10-foot ladder is leaning against the wall. The bottom of the ladder is 4 feet from the base of the wall. Which of the following is closest to the distance from the top of the ladder to the base of the wall?

a)

9ft

b)

11ft

c)

6ft

d)

14ft

102.

Solve for x. SIMPLIFY your radical answer completely.

a)

2√6

b)

6√2

c)

4√6

d)

6√4

103.

Solve for x. SIMPLIFY your radical answer completely.

a)

4√2

b)

2√4

c)

2√2

d)

16√2

104.

Solve for x. SIMPLIFY your radical answer completely.

a)

√3

b)

3

c)

√41

d)

41

105.

If a right triangle has a hypotenuse with a length of 12 cm and a leg with a length of 10 cm, how long is the other leg, simplify the radical.

a)

$2\sqrt{11}cm.$

b)

$11\sqrt{2}cm.$

c)

$4\sqrt{11}cm.$

d)

$11\sqrt{4}cm.$

106.

Simplify:
√200

a)

10√2

b)

2√10

c)

50√2

d)

2√50

107.

Simplify √125

a)

√125

b)

5√3

c)

3√5

d)

5√5

108.

Simplify √16

a)

4

b)

8

c)

16

d)

64

109.

What is the length of the iPad diagonal?

a)

$9\sqrt{2}in.$

b)

$\sqrt{85}in.$

c)

$\sqrt{13}in.$

d)

$5\sqrt{17}in.$

110.

A 12ft ladder leans against the side of a house. The bottom of the ladder is 8ft from the side of the house. How high is the ladder from the ground. Simplify the radical.

a)

$16\sqrt{5}ft.$

b)

$8ft.$

c)

$4\sqrt{5}in.$

d)

$4\sqrt{5}ft.$

111.

√96

a)

4√6

b)

3√6

c)

6√5

d)

6√8

112.

Simplify √18

a)

3√2

b)

9√2

c)

3√9

d)

2√3

113.

The perimeter of the following equilateral triangle is 30 units. Find the length of the altitude of the triangle. Simplify the radical.

a)

$\sqrt{75}$

b)

$25\sqrt{3}$

c)

$5\sqrt{3}$

d)

$10\sqrt{3}$

114.

Find the value of x.

a)

7

b)

8

c)

9

d)

10

115.

Find the value of x.

a)

36

b)

12

c)

16

d)

25

116.

Find the value of x.

a)

15

b)

16

c)

18

d)

17

117.

Does the set of numbers represent a Pythagorean Triple.
4, 5, 6

a)

Yes

b)

No

118.

Does the set of numbers represent a Pythagorean Triple.
10, 24, 26

a)

Yes

b)

No

119.

Does the set image show a Pythagorean Triple.

a)

Yes

b)

No

120.

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

a)

Yes

b)

No

c)

Maybe

d)

Pythagoras

121.

Does the set of numbers represent a Pythagorean Triple. $\sqrt[]{2},\ 1,\ 1$

a)

Yes

b)

No

122.

What is the hypotenuse if two sides are 6 and 8?

a)

10

b)

12

c)

13

d)

not enough information

123.

If 36 and 48 are the two smaller numbers in a Pythagorean Triple, what is the third number?

a)

45

b)

50

c)

55

d)

60

124.

Determine if the following set of numbers are Pythagorean Triples.
15, 20, 25

a)

Yes

b)

No

125.

Determine if the following set of numbers are Pythagorean Triples.
18, 73, 75

a)

Yes

b)

No

126.

Find the length of the missing side.

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

127.

Find the length of the missing side.

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

128.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

129.

solve for c

a)

7

b)

9

c)

4

d)

13

130.

Which of the following sets do NOT form a Pythagorean Triple? Select all that apply

a)

10, 24, 26

b)

9, 12, 15

c)

30, 40, 50.5

d)

9, 41, 42

131.

What is the measure of x?

a)

12

b)

15

c)

6

d)

9

132.

The triangles are similar, solve for the question mark.

a)

8

b)

12.5

c)

18

d)

24

133.

$\Delta ABC\sim\Delta ADE$
Find x.

a)

7

b)

8

c)

9

d)

10

134.

solve for x

a)

26

b)

27.6

c)

25.2

d)

28.8

e)

30.4

135.

a)

3

b)

9

c)

6

d)

12

e)

5

136.

a)

36

b)

42

c)

48

d)

52

e)

56

137.

a)

12.5

b)

18

c)

20

d)

22.5

e)

25

138.

a)

15

b)

13

c)

11

d)

17

139.

A tree is 72 feet tall and has a shadow that is 12 feet long. A nearby tree has a shadow of 5 feet. How tall is the tree?

a)

3 ft.

b)

300 ft.

c)

30 ft.

d)

35 ft.

140.

a)

The flagpole is 51 feet tall.

b)

The flagpole is 141.6 feet tall

c)

The flagpole is 14.16 feet tall

d)

The flagpole is 75 feet tall.

141.

These triangles are similar. What is the value of x?

a)

2 ft

b)

3 ft

c)

4 ft

d)

6 ft

142.

What is the value of x?

a)

3

b)

1.5

c)

8

d)

2/3

143.

Find YX.

a)

30

b)

25

c)

15

d)

40

144.

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

145.

What is the ratio from ΔABC to ΔDEF?

a)

1/2

b)

7/3

c)

2

d)

10/3

146.

These triangles are similar. What is the length of segment DF?

a)

18.3

b)

31.5

c)

13

d)

14

147.

a)

7

b)

12

c)

6

d)

4

148.

Find the value of X.

a)

4

b)

6

c)

12

d)

7

149.

ABCDE ∼ GHJDF. ∠E ≅

a)

∠H

b)

∠D

c)

∠F

d)

∠J

150.

State if the polygons are similar.

a)

a

b)

b

151.

State if the polygons are similar.

a)

a

b)

b

152.

The scale factor of RSTU to VWXY is 14:3. What is the scale factor of VWXY to RSTU?

a)

3: 14

b)

14: 6

c)

28: 3

d)

7: 1

153.

Two equilateral triangles are ___ similar.

a)

always

b)

sometimes

c)

never

154.

$\Delta PRQ\ \sim\ \Delta DEF$
What is $m\angle D$ ?

a)

35

b)

89

c)

56

d)

40

155.

$\Delta PRQ\ \sim\ \Delta DEF$
What is $m\angle R$ ?

a)

35

b)

89

c)

56

d)

40

156.

$\Delta PRQ\ \sim\ \Delta DEF$
What is $m\angle F$ ?

a)

35

b)

89

c)

56

d)

40

157.

$\angle CSE\cong\angle RST$ because of the ...

a)

Vertical Angles Theorem

b)

Angle Addition Postulate

c)

definition of Linear Pair

d)

because it looks like it

158.

Given that Ray QP bisects Angle RQS and RQ is congruent to QS, what allows you to say that $\angle RQP\cong\angle SQP$ ?

a)

Definition of Congruent Angles

b)

Vertical Angles Theorem

c)

Definition of Angle Bisector

d)

Alternate Interior Angles Theorem

159.

What would be the correct "given" statements for this diagram?

a)

T is the midpoint of segment BG and
∡B≅∡G

b)

∡B≅∡G and ∡A≅∡W

c)

T is the midpoint of segment BG and ∡A≅∡W

d)

T is the midpoint of segment AW and ∡A≅∡W

160.

Using the picture, $\overline{OE}\cong\overline{OE}$ , which property allows this?

a)

Definition of Congruent Segments

b)

Transitive Property

c)

Symmetric Property

d)

Reflexive Property

161.

Given that S is the midpoint of $\overline{TC}$ , what conclusion can you make?

a)

$\overline{RS}\cong\overline{ES}$

b)

$\overline{TS}\cong\overline{CS}$

c)

$\overline{RT}\cong\overline{EC}$

d)

point S bisects $\overline{RE}$

162.

Given $\overline{EJ}$ bisects $\overline{FH}$ , what can you conclude?

a)

$\overline{EG}\cong\overline{JG}$

b)

$\angle G\cong\angle G$

c)

$\overline{FG}\cong\overline{HG}$

d)

$\angle E\cong\angle J$

163.

Given $\overline{RN}\ \perp\overline{\ EV}$ what can you conclude?

a)

$\overline{EN}\cong\overline{VN}$

b)

$\angle RNE$ and $\angle RNV$ are right angles

c)

$\overline{RN}\cong\overline{RN}$

d)

$\angle E\cong\angle V$

164.

Given $\overline{PQ}\ \parallel\ \overline{RS}$ , what can you conclude?

a)

$\overline{RP}\cong\overline{QS}$

b)

$\overline{PQ}\cong\overline{SR}$

c)

$\angle SQR\cong\angle PRQ$

d)

$\angle PQR\cong\angle SRQ$

165.

If you know that angles 1 and 2 are vertical, what else do you know?

a)

Angles 1 and 2 are congruent

b)

Angles 1 and 2 are supplementary

c)

Angles 1 and 2 are right angles

d)

Angles 1 and 2 are corresponding angles

166.

If $AD$ bisects $\angle EDI$ , then...

a)

$\angle ADE\cong ADI$

b)

$IA\cong AE$

c)

$ID\ \cong ED$

d)

All of the above

167.

Given:

\overline{AD}

\parallel

\overline{BC}

, then what reason to <1 is congruent to <2 ?

a)

congruent same side interior angles since lines are parallel

b)

congruent corresponding angles since lines are perpendicular

c)

congruent angles since there is an angle bisector

d)

congruent alternate interior angles since lines are parallel

168.

Given AB is parallel to CD and AE is a transversal, make the best conclusion based on this information.

a)

<B is congruent to <DCE since they are alternate interior and lines are parallel

b)

Segment AC is congruent to Segment CE

c)

< BCA is congruent to <DEC since they are corresponding and lines are parallel

d)

<BAC is congruent to <DCE since they are corresponding and lines are parallel

169.

Using the following information determine the statements that are true, select all that apply:

X is the midpoint of $\overline{AY}$
$\overline{AX}\perp\overline{BX}$

\overline{XY}\ \perp\ \overline{YZ}

a)

segment AX is congruent to segment XY

b)

segment BX is congruent to segment ZY

c)

<BXA is 90 degrees

d)

<ZYX is 90 degrees

e)

< A is congruent to < ZXY

170.

Which pieces of information could you use to prove the triangles congruent? (Select multiple.)

a)

m∠Q = m∠S

b)

m∠P = m∠R

c)

m∠POQ = m∠ROS

d)

SO = QO

e)

RO = PO

171.

The altitudes of a triangle intersect at the _________________________.

a)

Centriod

b)

Circumcenter

c)

Incenter

d)

Orthocenter

172.

The orthocenter can be outside the triangle if the triangle is ...

a)

obtuse

b)

acute

c)

iscolese

d)

right

173.

10. What type of lines are shown

a)

perpendicular bisectors

b)

medians

c)

altitudes

d)

angle bisectors

174.

13. Which line is an altitude?

a)

XY

b)

BY

c)

AZ

d)

XC

175.

A segment joining a vertex to the opposite side so that is perpendiuclar to that side.

a)

perpendicular bisector

b)

angle bisector

c)

median

d)

altitude

176.

The ORTHOCENTER is the intersection of which special segments?

a)

Angle Bisectors

b)

Perpendicular Bisectors

c)

Medians

d)

Altitudes

177.

The figures above are examples of ...

a)

altitudes

b)

perpendicular bisectors

c)

medians

d)

angle bisectors

178.

Which center of a triangle is shown in the picture below?

a)

Circumcenter

b)

Orthocenter

c)

Incenter

d)

Centroid

179.

Segment BH is an example of which of the following?

a)

Perpendicular Bisector

b)

Altitude

c)

Median

d)

Midsegment

180.

Fill in the blank.
Altitudes hit the ground at _______ degrees.

a)

180

b)

90

c)

60

d)

360

181.

Select the triangle that shows the height that goes with the base shown here.

a)

b)

c)

182.

Select the triangle that shows the height for the base shown here.

a)

b)

c)

183.

Select the triangle that shows the height for the base shown here.

a)

b)

c)

184.

Which of the following statements are true?

a)

$\overline{BH}$ is perpendicular to $\overline{AC}$

b)

$m\angle ABH=90\degree$

c)

$\Delta CBH$ is a right triangle

d)

$\overline{AH}\ \cong\overline{HC}$

e)

$m\angle CHB=90\degree$

185.

Segment HK is an altitude in ΔGHI.

Find the value of x.

a)

90

b)

43.5

c)

24

d)

21

186.

What is the only special triangle segment that does not have to go through a vertex?

a)

Median

b)

Altitude

c)

Angle Bisector

d)

Perpendicular Bisector

187.

What type of special segment is shown?

a)

Median

b)

Perpendicular Bisector

c)

Angle Bisector

d)

Altitude

188.

What type of special segment is shown?

a)

Angle Bisector

b)

Altitude

c)

Median

d)

Perpendicular Bisector

189.

What type of special segment is shown?

a)

Median

b)

Angle Bisector

c)

Perpendicular Bisector

d)

Altitude

190.

What type of special segment is shown?

a)

Altitude

b)

Median

c)

Perpendicular Bisector

d)

Angle Bisector

191.

What type of special segment is shown?

a)

Perpendicular Bisector

b)

Angle Bisector

c)

Median

d)

Altitude

192.

What type of special segment is shown?

a)

Altitude

b)

Perpendicular Bisector

c)

Median

d)

Angle Bisector

193.

What type of special segment is shown?

a)

Angle Bisector

b)

Altitude

c)

Median

d)

Perpendicular Bisector

194.

Which of the following describes a median of a triangle?

a)

A segment that passes through the middle of the triangle.

b)

A segment with endpoints at the vertex and midpoint of the opposite side.

c)

A segment that connects two midpoints of two sides.

d)

A segment that connects the vertex and the opposite side at 90 degrees.

195.

If AG = 2x + 21 and RE = x + 10.5,
what is NG?

a)

16

b)

8

c)

26.5

d)

10.5

196.

PQ is the perpendicular bisector of MN. What is QN?

a)

7

b)

14

c)

10.5

d)

28

197.

In ΔXYZ, YB, XC, and ZA are medians, and YC = 15.
Find the length of YZ.

a)

30

b)

15

c)

5

d)

7.5

198.

Given: XZ is the median, WY=14. Find XY.

a)

XY = 14

b)

XY = 7

c)

XY = 10

d)

XY = 28

199.

BE = 15. Find EG.

a)

10

b)

5

c)

22.5

d)

20

200.

Find the length of AB

a)

6

b)

11

c)

17

d)

68

201.

Point O is the circumcenter of the triangle. Find OB

a)

OB = 4

b)

OB = 6

c)

OB = 5.1

d)

Not enough information

202.

[Angle Bisectors and Incenter]
If m<BCA is 72, what is m<PCA?

a)

72

b)

48

c)

60

d)

36

203.

If m∠CAP = 34° , find ∠CAB.

a)

17°

b)

34°

c)

68°

d)

90°

204.

P is the incenter of triangle JKL. Find OP.

a)

8

b)

13

c)

17

d)

4

205.

Which center of a triangle is shown in the picture below?

a)

Circumcenter

b)

Orthocenter

c)

Incenter

d)

Centroid

206.

Which of the following statements are true?

a)

$\overline{BH}$ is perpendicular to $\overline{AC}$

b)

$m\angle ABH=90\degree$

c)

$\Delta CBH$ is a right triangle

d)

$\overline{AH}\ \cong\overline{HC}$

e)

$m\angle CHB=90\degree$

207.

17. What type of line is shown by CD

a)

Altitude

b)

perpendicular bisector

c)

median

d)

angle bisector

208.

Name a midsegment of triangle ABC

a)

segment AC

b)

segment DE

c)

segment AB

d)

segment BC

209.

Name a segment that has the same length as segment BD

a)

segment BE

b)

segment DE

c)

segment AD

d)

segment AC

210.

Does\ \ GH=\frac{1}{2\ }DF\ ?

a)

no

b)

yes

211.

What segment is parallel to EF?

a)

Segment PM

b)

Segment MN

c)

Segment NP

d)

Segment FG

212.

QR is a midsegment of triangle WUV. What is the length of segment QR?

a)

4

b)

8

c)

16

d)

32

213.

What is the measure of angle X?

a)

60

b)

40

c)

140

d)

100

214.

QR is a midsegment of triangle FGH. Solve for x.

a)

5.5

b)

11

c)

-5.5

d)

-11

215.

IJ is a midsegment of triangle MLN. What is the length of segment IJ?

a)

9

b)

6

c)

18

d)

0

216.

VW is a midsegment of triangle KIJ. What is the length of segment KI?

a)

-1

b)

-10

c)

18

d)

8

217.

Find the length of AB

a)

6

b)

11

c)

17

d)

68

218.

Name the parallel segment.

a)

CP

b)

CA

c)

CB

d)

AB

219.

Name the parallel segment.

a)

JH

b)

PN

c)

MP

d)

MN

220.

What is the value of y?

a)

3

b)

-3

c)

No Solution

d)

5

221.

Find segment AB

a)

4

b)

16

c)

8

d)

12

222.

Find the length of QR

a)

11

b)

22

c)

24

d)

55

223.

Find the measure of angle SUP

a)

55 degrees

b)

125 degrees

c)

180 degrees

d)

not enough information

224.

The altitudes of a triangle intersect at the _________________________.

a)

Centriod

b)

Circumcenter

c)

Incenter

d)

Orthocenter

225.

The orthocenter can be outside the triangle if the triangle is ...

a)

obtuse

b)

acute

c)

iscolese

d)

right

226.

Segment HK is an altitude in ΔGHI.

Find the value of x.

a)

90

b)

43.5

c)

24

d)

21

227.

Name the segment/line/ray shown in the picture.

a)

Perpendicular Bisector

b)

Angle Bisector

c)

Median

d)

Altitude

228.

Select the triangle that shows the height for the base shown here.

a)

b)

c)

229.

Which of the following statements are true?

a)

$\overline{BH}$ is perpendicular to $\overline{AC}$

b)

$m\angle ABH=90\degree$

c)

$\Delta CBH$ is a right triangle

d)

$\overline{AH}\ \cong\overline{HC}$

e)

$m\angle CHB=90\degree$

230.

Find the measure of $\angle NJZ$

a)

38

b)

90

c)

52

d)

128

231.

Find the measure of $\overline{QA}$

a)

4

b)

-4

c)

16

d)

28

232.

Find the measure of $\angle MFZ$

a)

10

b)

19

c)

21

d)

32 $\frac{1}{3}$

233.

Point A is the incenter of $\Delta PQR$ . Find each measure of $\angle YLA$

a)

21

b)

32

c)

37

d)

58

234.

Point A is the incenter of $\Delta YGL$ . Find the measure of $\angle YGA$

a)

21

b)

32

c)

37

d)

53

235.

Find the measure of CP

(a)

236.

$\angle WYZ$ Find the measure of

(a)

237.

Find the measure of QP

(a)

238.

if Q is the incenter of $\Delta JLN$ , find JQ. Round your answer to the nearest tenth (one decimal place)

(Hint: Use the Pythagorean Theorem in triangle JPQ.)

(a)

239.

Find the measure of AF

(a)

240.

If P is the incenter of $\Delta AEC$ , find the measure of PB. Round your answer to the nearest tenth (one decimal place).

(Hint: use the Pythagorean Theorem in the right triangle ABP.)

(a)

241.

If P is the incenter of $\Delta AEC$ , find the measure of $m\angle EAC$

(a)

242.

P is the incenter of triangle JKL. Find PO.

a)

13

b)

24

c)

30

d)

31

243.

The sides of an equilateral triangle have...

a)

different measures.

b)

larger measures

c)

equal measures.

d)

60°.

244.

What do the angles in an equilateral triangle measure?

a)

30, 60, 90

b)

60, 60, 60

c)

45, 45, 90

d)

35, 55, 90

245.

If two sides of a triangle are congruent, then the _________________ opposite those sides are congruent.

a)

sides

b)

vertices

c)

angles

d)

measures

246.

Find x

a)

10

b)

32

c)

116

d)

16

247.

Find the value of x. (Hint: what kind of triangle is this?)

a)

$114\degree$

b)

$66\degree$

c)

$48\degree$

d)

$24\degree$

248.

Triangle LMN is isosceles, angle L is the vertex angle, LM = 3x – 2, LN = 2x + 1, and MN = 5x – 2.

Find the value of x.

(Hint: draw a picture)

a)

0

b)

1

c)

2

d)

3

249.

What is the length of side JK?

a)

12

b)

30

c)

33

d)

3

250.

Find x

a)

60

b)

48

c)

30

d)

28

251.

Find the value of y?

a)

16

b)

12

c)

4

d)

8

252.

What is the value of y?

a)

14

b)

4

c)

6

d)

7

253.

What is the value of x?

a)

60

b)

20

c)

15

d)

40

254.

Use the picture to answer the question.

a)

76

b)

28

c)

152

d)

56

255.

Find the values of m and n. [Ans: m, n]

a)

54, 27

b)

27, 27

c)

27, 36

d)

36, 27

256.

Find the measure of m<ACB

(a)

257.

Find the value of y.

(a)

258.

Find the measure of <ABC

(a)

259.

Which of the following angles are remote interior angles to angle d?

a)

Angle a and Angle b

b)

Angle b and Angle c

c)

Angle a and Angle c

d)

Angle a and Angle b and Angle c

260.

Which of the following terms best describes Angle d?

a)

Remote interior angle

b)

Corresponding angle

c)

Exterior angle

d)

Interior angle

261.

What is the measure of angle b?

a)

36^o

b)

56^o

c)

63^o

d)

117^o

262.

Find the value of x.

a)

A

b)

B

c)

C

d)

D

263.

Find the value of x.

a)

A

b)

B

c)

C

d)

D

264.

Find the measure of angle x.

a)

138

b)

96

c)

93

d)

87

265.

Find the measure of each angle indicated.

a)

88

b)

30

c)

110

d)

85

266.

Find the measure of each angle indicated.

a)

48

b)

87

c)

35

d)

40

267.

Solve for x.

a)

6

b)

8

c)

15

d)

13

268.

What is the measure of angle A in the triangle?

a)

116*

b)

25*

c)

62*

d)

54*

269.

Solve for x

a)

48

b)

85

c)

24

d)

9

Question Bank for Grade 9 Mathematics

Total questions: 269

Worksheet time: 15hrs 7mins

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