Free Printable Math triangle

1.

In this 45-45-90 triangle, I have been given a leg, so to find the other leg I...

a)

Multiply that leg by 2

b)

Use the same length for the second leg

c)

Multiply that leg by √2

d)

Divide that leg by √2

2.

What is the length of y in this picture?

a)

45

b)

5√2

c)

90

d)

5

3.

In this 45-45-90 triangle, I have been given the length of a leg. How do I find the length of the hypotenuse?

a)

It is the same length as the given leg.

b)

Multiply that leg's length by √2.

c)

Multiply that leg's length by 2.

d)

Divide that leg's length by √2.

4.

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

a)

4√2

b)

4

c)

8

d)

4√3

5.

I have been given a hypotenuse in this 45-45-90 triangle. How do I find the length of a leg of the triangle?

a)

Multiply by √2

b)

Divide by √2

c)

It's the same length as the hypotenuse.

d)

Divide by 2

6.

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

a)

8√2

b)

4√2

c)

4

d)

8

7.

Which side is the long leg in this 30-60-90 triangle?

a)

4

b)

u

c)

v

8.

Which side is the short leg of this 30-60-90 triangle?

a)

6

b)

m

c)

n

9.

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

a)

Multiply 4 by 2

b)

Multiply 4 by √3

c)

Multiply 4 by √2

d)

Divide 4 by 2

10.

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

11.

Find the value of y.

a)

8

b)

4

c)

2√3

d)

8√3

12.

Choose the correct values for x and y in the right triangle.

a)

$x=12$

b)

$x=12\sqrt{2}$

c)

$y\ =\ 24$

d)

$y=12\sqrt{2}$

13.

Choose the correct values for x and y in the right triangle.

a)

$x=12$

b)

$x=12\sqrt{2}$

c)

$y\ =\ 24$

d)

$y=12\sqrt{2}$

14.

Choose the correct values for x and y in the right triangle.

a)

$x=18$

b)

$x=9\sqrt{2}$

c)

$y\ =\ 9$

d)

$y=9\sqrt{2}$

15.

Choose the correct values for x and y in the right triangle.

a)

$x=14$

b)

$x=7\sqrt{2}$

c)

$y\ =\ 7$

d)

$y=7\sqrt{2}$

16.

Choose the correct values for x and y in the right triangle.

a)

$x=3$

b)

$x=3\sqrt{2}$

c)

$y\ =\ 6$

d)

$y=6\sqrt{2}$

17.

Choose the correct values for x and y in the right triangle.

a)

$x=3\sqrt{3}$

b)

$x=6$

c)

$y\ =\ 3\sqrt{3}$

d)

$y=6$

18.

Choose the correct values for x and y in the right triangle.

a)

$x=\frac{5\sqrt{6}}{2}$

b)

$x=5$

c)

$y\ =\ 10$

d)

$y=10\sqrt{3}$

19.

Choose the correct values for x and y in the right triangle.

a)

$x=\frac{11\sqrt{3}}{3}$

b)

$x=11$

c)

$y\ =\ 22$

d)

$y=11\sqrt{3}$

20.

Choose the correct values for x and y in the right triangle.

a)

$x=6\sqrt{3}$

b)

$x=9$

c)

$y\ =\ 3\sqrt{6}$

d)

$y=6\sqrt{3}$

21.

What type of special triangle is this?

a)

45°-45°-90°

b)

30°-60°-90°

c)

Equiangular

d)

Equilateral

22.

What type of special triangle is this?

a)

45°-45°-90°

b)

30°-60°-90°

c)

Isosceles

d)

Obtuse

23.

Find x.

a)

30°

b)

45°

c)

60°

d)

90°

24.

In this 45-45-90 triangle, I have been given a leg, so to find the other leg I...

a)

Multiply that leg by 2

b)

Use the same length for the second leg

c)

Multiply that leg by √2

d)

Divide that leg by √2

25.

In this 45-45-90 triangle, I have been given the length of a leg. How do I find the length of the hypotenuse?

a)

It is the same length as the given leg.

b)

Multiply that leg's length by √2.

c)

Multiply that leg's length by 2.

d)

Divide that leg's length by √2.

26.

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

a)

Multiply 4 by 2

b)

Multiply 4 by √3

c)

Multiply 4 by √2

d)

Divide 4 by 2

27.

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

28.

What is the length of u and v in this 30-60-90 triangle?

a)

u = 8 v = 4√3

b)

u = 4√2 v = 8

c)

u = 16 v = 8

d)

u = 4√3 v = 8

29.

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

a)

Multiply 7 by 2

b)

Multiply 7 by √3

c)

Divide 7 by 2

d)

Divide 7 by √3

30.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

31.

The legs form what type of angle?

a)

Acute

b)

Obtuse

c)

Reflex

d)

Right

32.

Which set of sides would make a right triangle?

a)

4,5,6

b)

8,10,12

c)

5,12,13

d)

5,10,12

33.

What is the opposite of squaring a number?

a)

divide

b)

multiply

c)

fractions

d)

square root

34.

What is the distance from the base of the house to the base of the ladder?

a)

25 m

b)

5 m

c)

313 m

d)

17.7 m

35.

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

36.

Why do we use the Pythagorean Theorem?

a)

To find the missing side of a right triangle

b)

To find the area of a triangle

c)

To find the volume of a cone

d)

To find the circumference of a circle

37.

What is the formula used for the Pythagorean Theorem?

a)

a + b = c

b)

a² + b² = c²

c)

a₂ + b₂ = c₂

d)

a x b = c

38.

What is the hypotenuse (c)?

a)

the two sides that make up the right angle

b)

the longest side, across from the right angle

c)

the shortest side

d)

the straight side of the triangle

39.

Using the Pythagorean Theorem, find the area of the missing square (seen in picture)

a)

30 cm²

b)

15 cm²

c)

315 cm²

d)

45 cm²

40.

Using the Pythagorean Theorem, find the area of the missing square (seen in picture)

a)

75 cm²

b)

105 cm²

c)

135 cm²

d)

30 cm²

41.

Can these three squares be arranged to make a right triangle?

a)

Yes, they would form a right triangle

b)

No, they would not form a right triangle

42.

Using the Pythagorean Theorem, find the length of the missing side of the triangle pictured:

a)

12.12

b)

21.2

c)

7.3

43.

Using the Pythagorean Theorem, find the length of the missing side of the triangle pictured:

a)

23

b)

17

c)

7

44.

If a boat sailed six miles north and eight miles east, how far away is it from its original location? (find d)

a)

100 miles

b)

14 miles

c)

10 miles

d)

2 miles

45.

If the ramp is 21 feet long, and ends 19 feet away from the building, how high (h) is the ramp?

a)

2.19 ft

b)

8.9 ft

c)

28.3 ft

46.

Which equation is modeled by the picture shown?

a)

3²+5²=4²

b)

3²+4²=5²

c)

5²+4²=3²

d)

9²+16²=25²

47.

If a square has an area of 88 in², what is the side length of the square?

a)

22 in because I divided 88 by 4

b)

7744 in⁴ because I squared 88

c)

44 in because I divided 88 by 2

d)

9.38 in because I took the square root of 88

48.

What is the length of the hypotenuse?

a)

33.5 cm

b)

45 cm

c)

6.7 cm

d)

15 cm

49.

How far does the catcher throw the ball from home plate to 2nd base?

a)

63.6 ft

b)

16,129 ft

c)

13.4 ft

d)

127.3 ft

50.

If 231 square feet of paint was used to paint the two squares blue, how much paint would be needed to paint the white square purple?

a)

15.2 ft²

b)

115.5 ft²

c)

231 ft²

d)

10.7 ft²

51.

Find the value of x.

a)

49

b)

85

c)

121

d)

140.3

e)

44.6

52.

Find the value of w and x.

a)

w = 16, y = 2

b)

w = 2, y = 17

c)

w = 3, y = 15

d)

w = 2, y = 18

e)

w = 2, y = 16

53.

To find the clearance under an overpass, you need to find the height of a concrete support beam. You use a cardboard square to line up the top and bottom of the beam. Your friend measures the vertical distance from you to the beam. What is the approximate height of the beam?

a)

9.5 feet

b)

47.6 feet

c)

3.6 feet

d)

14.5 feet

e)

8.6 feet

54.

Find the value of x.

a)

21

b)

3

c)

81

d)

9

e)

18

55.

Find the value of y.

a)

6

b)

108

c)

$6\sqrt{6}$

d)

$3\sqrt{6}$

e)

3

56.

$\overline{BD}$ is the altitude of $\Delta ABC$ . If AD=25, BD=10, then what is AC?

a)

5

b)

4

c)

$5\sqrt{10}$

d)

29

e)

$10\sqrt{5}$

57.

A cross section of a group of seats at a stadium shows a drainage pipe $\overline{BD}$ that leads from the seats to the inside of the stadium. What is the approximate length of the pipe?

a)

60 feet

b)

16.6 feet

c)

3.6 feet

d)

15.6 feet

e)

10.3 feet

58.

Find the value of a, b, and c.

a)

a = 20, b = 25, and c = 15

b)

a = 15, b = 25, and c = 20

c)

a = 15, b = 16, and c = 20

d)

a = 16, b = 20, and c = 25

e)

a = 25, b = 15, and c = 20

59.

In the diagram, AC = 25 and BC = 13. Find AD. Round to the nearest tenth.

a)

18.2

b)

16.9

c)

13

d)

6.8

e)

15.5

60.

Given triangles are similar. Find missing side.

a)

5

b)

7

c)

9

d)

11

61.

Complete each proportion.
CB / DM = AC / ?

a)

BM

b)

MA

c)

BC

d)

AD

62.

Choose the similarity statement for the triangles.

a)

ΔMNL ∼ ΔOPQ

b)

ΔNOM ∼ ΔPQL

c)

ΔLMN ∼ ΔPQO

d)

ΔMLN ∼ ΔPQO

63.

Which of the following is NOT true about similar figures?

a)

A) Similar figures always have the same shape.

b)

B) Similar figures always have the same size.

c)

C) Similar figures always have corresponding angles that are equal.

d)

D) Similar figures always have corresponding sides that are proportional.

64.

in the fig, if DE ll BC then find the value of AD

a)

16

b)

8

c)

4

d)

32

65.

What is the measure of x?

a)

12

b)

15

c)

6

d)

9

66.

The triangles are similar, solve for the question mark.

a)

8

b)

12.5

c)

18

d)

24

67.

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

a)

SAS

b)

AA

c)

SSS

d)

not similar

68.

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

a)

AA

b)

SSS

c)

SAS

d)

no similar

69.

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

a)

SSS

b)

AA

c)

SAS

d)

not similar

70.

What similarity theorem would prove that these triangles are similar?

a)

SAS∼

b)

SSS∼

c)

AA∼

d)

Side Splitter

71.

Are the triangles similar?

a)

Yes

b)

No

72.

A triangle has sizes measuring 11 cm, 16 cm, and 16 cm. A similar triangle has sides measuring x cm, 24 cm, and 24 cm. What is x?

a)

x = 19 cm

b)

x = 24 cm

c)

x = 3 cm

d)

x = 16.5 cm

73.

What similarity theorem would you use to prove these triangles are similar?

a)

SAS∼

b)

SSS∼

c)

AA∼

d)

BUCK∼

74.

State the postulate that proves these triangles are similar.

a)

SSS

b)

AA

c)

SAS

d)

Not similar

75.

Find side length X.

a)

16

b)

18

c)

2.4

d)

15

76.

Find side length X.

a)

30

b)

25

c)

15

d)

40

77.

Find side length X.

a)

22.5

b)

10

c)

9

d)

7.5

78.

How do these triangles appear to be similar?

a)

AA

b)

SAS

c)

SSS

d)

Not Similar

79.

How do these triangles appear to be similar?
(Hint: Look for non-labeled parts!)

a)

AA

b)

SAS

c)

SSS

d)

Not Similar

80.

How do these triangles appear to be similar?
(Hint: Look for non-labeled parts!)

a)

AA

b)

SAS

c)

SSS

d)

Not Similar

81.

If two triangles are similar their angles are______.

a)

proportional

b)

congruent

c)

supplementary

d)

complementary

82.

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

a)

equal

b)

congruent

c)

proportional

d)

none of these

83.

Complete each proportion.
CB / DM = AC / ?

a)

BM

b)

MA

c)

BC

d)

AD

84.

Complete each proportion.

AB / AM = ? / AD

a)

BC

b)

AC

c)

MD

d)

MC

85.

What is the scale factor from ΔABC to ΔDEF?

a)

1/2

b)

7/3

c)

2

d)

10/3

86.

If the two triangles are similar, what is the measurement of x?

a)

16

b)

18

c)

2.4

d)

15

87.

A telephone booth that is 8 ft tall casts a shadow that is 4 ft long. Find the height of a lawn ornament that casts a 2 ft shadow.

a)

4 ft

b)

2 ft

c)

8 ft

d)

6ft

88.

A map has a scale of 3 cm:18km. If Oakdale and Woodridge are 54 km apart, then they are how far apart on the map?

a)

15 cm

b)

8.7 cm

c)

9 cm

d)

6 cm

89.

Figure A is enlarged to figure B. Find the scale factor.

a)

2.5

b)

3

c)

0.4

d)

6

Math triangle

Total questions: 89

Worksheet time: 4hrs 16mins

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