Free Printable Pythagorean Theorem

1.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

2.

What side(s) will always be the longest on a right triangle?

a)

The Hypotenuse

b)

Leg A

c)

Leg B

d)

The Right Angle

3.

What side(s) will always be the shortest on a right triangle?

Select all that apply

a)

The Hypotenuse

b)

Leg A

c)

Leg B

d)

The Right Angle

4.

The legs form what type of angle?

a)

Acute

b)

Obtuse

c)

Reflex

d)

Right

5.

What is the relationship between the sides in the Pythagorean Theorem shown?

Hint: Think about when the hypotenuse is missing!

a)

a + b = c

b)

a² + b² = c²

c)

a² – b² = c²

d)

a – b = c

6.

Do three squares with side lengths of 6, 12, and 13 form a right triangle?

a)

Yes

b)

No

7.

If three sides of a right triangle are 9, 40, and 41, which side is the hypotenuse?

a)

9

b)

40

c)

41

8.

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

a)

Yes

b)

No

9.

Do these 3 side lengths form a right triangle?
13, 80, and 81?

a)

yes

b)

no

10.

If the sides of a triangle are 7, 24, and 25, is it a right triangle?

a)

yes

b)

no

11.

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

a)

yes

b)

no

12.

Isabella has sticks that are 10cm, 11cm, and 13cm long. Can she place the sticks together to form a right triangle? Justify your answer.

a)

No, because 10+11 does not equal 13

b)

No, because 100+121 does not equal 169

c)

Yes, because there is a small side, medium side and long side

d)

Yes, because a triangle has 3 sides

13.

Drag the correct letter to the box.

a)B

b)A

c)C

1

1)

14.

The (a) of the (b) created by the legs of a (c) triangle are (d) to the area of the square created by the (e) .

Choose from the below words

sum

areas

right

equal

hypotenuse

15.

Which set of side lengths would form a right triangle?

a)

6, 9, 12

b)

8, 10, 12

c)

9, 40, 41

d)

5, 10, 12

16.

A rectangular high jump pit is 25 feet long and 10 feet wide. Which of these is closest to the diagonal distance across the pit?

a)

25 feet

b)

26 feet

c)

27 feet

d)

28 feet

17.

Which equation will help you find the missing side?

a)

$4^2+10^2=c^2$

b)

$10^2-4^2=c^2$

c)

$c^2=100+10^2$

d)

$c^2+4^2=10^2$

18.

Which of these is closest to the length of PQ?

a)

10.9 units

b)

13 units

c)

2.4 units

d)

169 units

19.

Please read the question carefully:

a)

A

b)

B

c)

C

d)

D

20.

Please read the question carefully:

a)

A

b)

B

c)

C

d)

D

21.

Find the distance between these 2 points.

a)

5.8

b)

6.3

c)

8.1

d)

40

22.

A rectangular pool at Andy's gym measures 25 m by 50 m. How far would Andy swim if he swims across the pool diagonally?

a)

5 m

b)

8.7 m

c)

43.3 m

d)

55.9 m

23.

The Pythagorean Theorem is (a) (b) (c) (d) (e)

Choose from the below words

$a^2$

$+$

$b^2$

$=$

$c^2$

$x^2$

$-$

$\times$

$\div$

24.

What letter represents the hypotenuse?

a)

a

b)

b

c)

a and b

d)

c

25.

Hypotenuse

a)

Vertical side in a right triangle

b)

Longest side in a right triangle

c)

Horizontal side in a right triangle

d)

a²+ b²= c²

26.

Which choice represents the legs?

a)

a and b

b)

a

c)

b

d)

c

27.

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

28.

The Pythagorean Theorem is

a² - b² = c²

a)

false

b)

true

29.

Side c on a right triangle is ALWAYS the longest.

a)

true

b)

false

30.

What is the opposite of squaring a number?

a)

divide

b)

multiply

c)

fractions

d)

square root

31.

Side a on a right triangle is ALWAYS the longest side

a)

true

b)

false

32.

If you are solving to find a missing leg, should you add or subtract?

a)

Add

b)

Subtract

33.

If you are solving to find a missing hypotenuse, should you add or subtract?

a)

Add

b)

Subtract

34.

_{^{Find the missing side}}

a)

9

b)

41

c)

6.4

d)

3

35.

Level 2

Solve for the value of y

a)

13

b)

5

c)

23

d)

10

36.

Find the distance between these two points.

a)

13

b)

7.9

c)

9.2

d)

3.6

37.

Draw a right triangle and label the sides using: Leg, Leg, Hypotenuse

38.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

39.

Find the length of the missing side.

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

40.

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

41.

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

a)

17 miles

b)

32 miles

c)

37 miles

d)

40 miles

42.

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

a)

yes

b)

no

43.

Find the length of the missing side.

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

44.

_{^{Find the missing side}}

a)

48

b)

108

c)

83.6

d)

72

45.

What is the formula for finding the hypotenuse?

a)

a²⁺b²=c²

b)

a+b=c

c)

a-b=c

d)

c-a=c

46.

_{^{Find the missing side}}

a)

37

b)

17.66

c)

6

d)

312

47.

Jane and Miguel are siblings. They go to different schools. Jane walks 6 blocks east from home. Miguel walks 8 blocks north. How many blocks apart would the two schools be if you could walk straight from one school to the other?

a)

14

b)

10

c)

5.3

d)

2

48.

The Pythagorean Theorem is
c² = a² - b²

a)

false

b)

true

49.

Sides a and b are called legs.

a)

true

b)

false

50.

Side c on a right triangle is ALWAYS the longest.

a)

true

b)

false

51.

_{^{Find the missing side}}

a)

9

b)

41

c)

6.4

d)

6.2

52.

Does the set of numbers represent a right triangle?

20, 25, 15

a)

Yes

b)

No

53.

Find the length of the missing side.

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

54.

Find the length of the missing side.

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

55.

Find the length of the missing side.

a)

48 in.

b)

52 in.

c)

16 in.

d)

24 in.

56.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

57.

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

58.

Two LEGS are 9 and 12. What is the hypotenuse?

a)

14

b)

15

c)

17

d)

18

59.

If each square is one mile, how many miles is it from the mall to the movies?

a)

3.6 miles

b)

2.4 miles

c)

3.3 miles

d)

4 miles

60.

Look at the model of the Pythagorean Theorem. What is the length of the side of the large green square?

a)

14 cm

b)

15 cm

c)

16 cm

d)

13 cm

61.

The leg of a triangle is 24 and its hypotenuse is 25. What is the length of its other leg?

a)

5

b)

12

c)

8

d)

7

62.

A model of the Pythagorean Theorem is shown. Which statement is true?

a)

If you add the areas of regions R and P they will add to the area of region Q

b)

If you add areas of regions R and Q they will add to the area of region P

c)

If you subtract the areas of regions Q and R they will make the area of region P

63.

Will the sides 29, 21, and 20 form a right triangle?

a)

yes

b)

no

64.

A right triangle has a hypotenuse of 25 and a leg of 15. What is the length of the other leg?

a)

20

b)

10

c)

12

d)

16

65.

Two legs of a right triangle are 20 and 21. What is the hypotenuse?

a)

28

b)

29

c)

30

d)

27

66.

If the hypotenuse of a right triangle is 50 and the leg is 14, what is the length of the other leg?

a)

48

b)

46

c)

45

d)

42

67.

Will the sides 36, 85 and 77 make a right triangle?

a)

yes

b)

no

68.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

69.

Side c on a right triangle is ALWAYS the longest side.

a)

TRUE

b)

FALSE

70.

How long is the hypotenuse of this triangle?

(a)

71.

Which sides are the legs of the triangle

a)

9 and 15

b)

9 and 12

c)

12 and 15

d)

15

72.

Is this a right triangle?

a)

YES

b)

NO

73.

Is this a right triangle?

a)

YES

b)

NO

74.

Is this a right triangle?

a)

YES

b)

NO

75.

Is a triangle with side lengths of 12, 9, and 15 a right triangle?

a)

YES

b)

NO

76.

Does a triangle with side lengths of 7, 4, and 4 have a 90 degree angle?

a)

YES

b)

NO

77.

Find the missing side.

a)

18

b)

16

c)

17

d)

19

78.

Find the missing side.

a)

11

b)

12

c)

13

d)

14

79.

A triangle has legs that are 7 inches and 24 inches long. How long is the hypotenuse?

a)

23

b)

26

c)

28

d)

25

80.

Does the set of numbers represent a right triangle?

20, 25, 15

a)

Yes

b)

No

81.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

82.

What is the opposite of squaring a number?

a)

divide

b)

multiply

c)

fractions

d)

square root

83.

Do the lengths form a right triangle? 6, 8, 10

a)

yes

b)

no

84.

_{^{Find the missing side}}

a)

36

b)

76.8

c)

12

d)

40

85.

solve for x

a)

5552363959656.

b)

10

c)

100

d)

89

86.

solve for the value of y

a)

13

b)

5

c)

23

d)

10

87.

solve for y

a)

7

b)

6.3

c)

2.5

d)

9

88.

solve for c

a)

7

b)

9

c)

4

d)

13

89.

An airplane flies 56 miles due north and then 33 miles due east. How many miles is the plane from its starting point?

a)

65 miles

b)

89 miles

c)

45.4 miles

d)

We don't have enough information.

90.

What is the length of x?

a)

5

b)

7

c)

8

d)

25

91.

_{^{Find the missing side}}

a)

9

b)

26.9

c)

37

d)

18.2

92.

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

a)

25 feet

b)

26 feet

c)

27 feet

d)

28 feet

93.

solve for the value of y

a)

13

b)

5

c)

23

d)

10

94.

The diagonal of a rectangle is 25 in. The width is 15 in. What is the length of the rectangle?

a)

20 inches

b)

29.2 inches

c)

400 inches

d)

625 inches

Pythagorean Theorem

Total questions: 94

Worksheet time: 6hrs 45mins

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