Free Printable Pythagorean Theorem Review

1.

Find the length of the missing side.

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

2.

Find the length of the missing side.

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

3.

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

4.

a² + b² = c^{2
a = 9 b = 40}

a)

c = 41

b)

c = 65

c)

c = 25

d)

c = 5

5.

a² + b² = c^{2
b = 35 c = 37}

a)

a = 12

b)

a = 11

c)

a = 18

d)

a = 14

6.

_{^{Find the missing side}}

a)

9

b)

41

c)

6.4

d)

3

7.

side a on a right triangle is ALWAYS the longest side

a)

true

b)

false

8.

What is the longest side of a right triangle called?

a)

Leg A

b)

Leg B

c)

Hypotenuse

d)

Pythagoras' Big Buddy

9.

State if the three sides lengths form an acute, obtuse, or right triangle:
6 mi, 14 mi, 17 mi

a)

acute

b)

obtuse

c)

right

10.

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

11.

State if the three sides lengths form an acute, obtuse, or right triangle:
7 in, 11 in, 13 in

a)

acute

b)

obtuse

c)

right

12.

The size of a television screen is measured by the length of the diagonal of the screen. What size is a television screen that is 3 feet tall and 6 feet wide?

a)

18

b)

6.7

13.

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

a)

5

b)

7

c)

10

d)

12

14.

a)

G

b)

O

c)

E

d)

X

15.

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

a)

yes

b)

no

16.

Would a triangle with these side lengths be a right triangle?
4, 5, 6

a)

Yes

b)

No

17.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

18.

What is the opposite of squaring a number?

a)

divide

b)

multiply

c)

fractions

d)

square root

19.

What is the side of a right triangle across from the right angle called?

a)

square

b)

arm

c)

leg

d)

hypotenuse

20.

Which of the following sentences would belong in the proof that describes this image?

a)

The sum of the areas of the two smaller squares is equal to the area of the large square.

b)

The sum of the side lengths of the two smaller squares is equal to the side length of the large square.

c)

The difference of the areas of the two smaller squares is equal to the area of the large square.

d)

The differences of the side lengths of the two smaller squares is equal to the side length of the large square.

21.

solve for c

a)

7

b)

9

c)

4

d)

13

22.

_{^{Find the missing side}}

a)

48

b)

108

c)

83.6

d)

72

23.

a)

The diagonal is 26 ft

b)

The diagonal is 31 ft

c)

The diagonal is 21.8 ft

d)

The diagonal is 20.9 ft

24.

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

25.

solve for x

a)

5552363959656.

b)

10

c)

100

d)

89

26.

What is the value of x in the right triangle shown?

a)

16cm

b)

18cm

c)

24cm

d)

√674cm

27.

Simplify

a)

9

b)

√9

c)

3√9

d)

can't simplify

28.

Which letter matches the coordinate (4, -6)?

a)

G

b)

Z

c)

K

d)

None of the above

29.

Which letter matches the coordinate (0, -6)?

a)

O

b)

L

c)

i

d)

Z

30.

On the coordinate plane, which line is the y-axis?

a)

Horizontal Line (Side to Side)

b)

Vertical Line (Up and Down)

31.

What letter is at (7, -6)?

a)

D

b)

L

c)

X

d)

There is no letter at those coordinates.

32.

Find the length of the missing side.

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

33.

Does the set of numbers represent a Pythagorean Triple?
14, 20, 24

a)

Yes

b)

No

34.

Find the distance.

a)

9.7

b)

10.7

c)

11.7

d)

12.7

35.

Find the distance between J and K.

a)

8.2

b)

7.7

c)

9

d)

10.2

36.

Find the distance between (-4, 5) and (7, 18).

a)

15.96

b)

16.08

c)

16.23

d)

17.03

37.

Find the distance between (-3, -11) and (8, -42).

a)

32.1

b)

32.3

c)

32.7

d)

32.9

38.

Find the distance between (3, 24) and (7, 56).

a)

32.1

b)

32.2

c)

32.4

d)

33.2

39.

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

a)

8.9

b)

9.8

c)

10.3

d)

11

40.

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

a)

24.05

b)

24.06

c)

24.07

d)

24.08

41.

What is the distance between (2,9) and (1,5)?

a)

15

b)

17

c)

4.12

d)

3.87

42.

Find the length of the missing side.

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

43.

Solve for x.

a)

38.9

b)

40.2

c)

45.6

d)

54

44.

Find the distance.

a)

7.1

b)

7.8

c)

8.7

d)

8.9

45.

What is the distance between (2,9) and (1,5)?

a)

15

b)

17

c)

4.12

d)

3.87

46.

What is the distance between the two points?

a)

6.3

b)

6.5

c)

6.7

d)

16

47.

Find the distance.

a)

9.7

b)

10.7

c)

11.7

d)

12.7

48.

Find the distance between (-4, 5) and (7, 18).

a)

15.96

b)

16.08

c)

16.23

d)

17.03

49.

Find the distance between (3, 24) and (7, 56).

a)

32.1

b)

32.2

c)

32.3

d)

32.4

50.

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

a)

8.9

b)

9.8

c)

10.3

d)

11

51.

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

a)

24.05

b)

24.06

c)

24.07

d)

24.08

52.

How is the distance formula correctly written:

a)

$d\ =\ \sqrt{\left(y_{1\ }-\ y_2\right)^2\ -\left(x_{2\ }-\ x_1\right)^2}\$

b)

$d\ =\ \sqrt{\left(x_{2\ }-\ x_1\right)^2\ +\ \left(y_{2_{\ }}-\ y_1\ \right)2}$

c)

$d\ =\ \sqrt{\left(y_{1\ }-\ y\ _2\right)^2\ +\ \left(x_{2\ }-\ x_1\right)}^2$

d)

d = $\sqrt{\left(x\right)^2-\ \left(y\right)^2}$

53.

A(3,1) B(-2,-1) written correctly is:

a)

$\sqrt{\left(-2-3\right)^2\ +\ \left(-1-1\right)^2}$

b)

$\sqrt{\left(1-3\right)^2\ +\ \left(-1-2\right)^2}$

c)

$\sqrt{\left(-2-3\right)^2\ -\ \left(-1-1\right)^2}$

d)

$\sqrt{\left(-2-3\right)^2\ -\ \left(-1-1\right)^2}$

54.

A(2,0) B(-2,4) is written as

a)

$d\ =\ \sqrt{\left(4-2\right)^2\ -\ \left(0-2\right)^2}$

b)

$d\ =\ \sqrt{\left(4-0\right)^2\ -\ \left(-2-2\right)^2}$

c)

$d\ =\ \sqrt{\left(-2\ +0\right)^2\ +\ \left(4+2\right)^2}$

d)

$d\ =\ \sqrt{\left(-2-2\right)^2\ +\ \left(4-0\right)^2}$

55.

7²

a)

50

b)

49

c)

14

d)

48

56.

√36

a)

3

b)

18

c)

6

d)

7

57.

9²

a)

81

b)

100

c)

80

d)

72

58.

8²

a)

16

b)

64

c)

24

d)

10

59.

√121

a)

12

b)

10

c)

11

d)

3

60.

√36

a)

4

b)

3

c)

6

d)

5

61.

√25

a)

2

b)

3

c)

5

d)

6

62.

√40 is between which two whole numbers? (integers)
¿Entre qué dos números enteros? (enteros)

a)

A. 5 and 6

b)

B. 6 and 7

c)

C. 7 and 8

d)

D. 39 and 41

63.

Which of the following is NOT a perfect square?
¿Cuál de los siguientes NO es un cuadrado perfecto?

a)

1

b)

4

c)

100

d)

8

64.

Estimate the square root.
Estime la raíz cuadrada.

a)

4

b)

5

c)

6

d)

7

65.

Estimate the square root.
Estime la raíz cuadrada.

a)

3

b)

4

c)

5

d)

6

66.

The area of a square is 36 cm². What is the length of one side?
El área de un cuadrado es 36 cm2. ¿Cuál es la longitud de un lado?

a)

6 cm

b)

24 cm

c)

9 cm

d)

9 cm

67.

What is the length of the side of the square with an area of 25 square feet?
¿Cuál es la longitud del lado del cuadrado con un área de 25 pies cuadrados?

a)

12.5 feet

b)

10 feet

c)

5 feet

d)

6 feet

68.

Which of the following is a perfect square?
¿Cuál de los siguientes es un cuadrado perfecto?

a)

24

b)

48

c)

81

d)

110

69.

√16

a)

4

b)

8

c)

2

d)

9

70.

What is a square root?
¿Qué es una raíz cuadrada?

a)

A number to the second power

Un número para la segunda potencia

b)

A square that has roots on it.

Un cuadrado que tiene raíces en él

c)

A number divided by 2

Un número dividido por 2

d)

Square roots are numbers that
produce a specified quantity when multiplied by itself]
Las raíces cuadradas son números que producir una cantidad específica cuando se multiplica por sí mismo

71.

The area of a square is 36 cm². What is the length of one side?
El área de un cuadrado es 36 cm2. ¿Cuál es la longitud de un lado?

a)

6 cm

b)

24 cm

c)

9 cm

d)

9 cm

72.

14²is called ________
14² se llama ________.

a)

14 cubed

14 cubos

b)

14 squared

14 al cuadrado

c)

14 to the 14th power

14 a la 14 potencia

d)

28

73.

Which would be the next number in the pattern?
36, 49, 64, 81 __
¿Cuál sería el próximo número en el patrón?
36, 49, 64, 81 __

a)

82

b)

18

c)

64

d)

100

74.

√13 is read?
√13 ¿es leído?

a)

Thirteen

Trece

b)

Thirteen squared

Trece cuadrados

c)

The square root of 13

La raíz cuadrada de 13

d)

Check mark 13

Marca de verificación 13

75.

a)

√81 = 9

b)

9 ÷ 9 = 1

c)

9 × 2 = 18

d)

√9 = 3

76.

Mrs. Hiltz and Ms. Weber decide to host a lemonade stand. The table they use has side lengths of 5 feet. What is the area of their table?

a)

25 feet

b)

25 square inches

c)

5 ft²

d)

25 square feet

77.

Mr. Jarowski is hanging a square picture frame that has ab area of 169 cm². Find the side length of the frame.

a)

12 cm

b)

13 cm

c)

13 in

d)

16 cm

78.

Mr. Sansonetti wants to buy the iPod shuffle. If the area of the iPod was 9 cm², how long was the side of the iPod shuffle?

a)

3 cm

b)

9 cm

c)

3 in

d)

4 cm

79.

The area of the square pool on Mr. Carr's vacation was 256 ft². How long was one side of the pool?

a)

17 ft

b)

18 ft

c)

16 ft

d)

15 ft

80.

Which number is closest to the approximate value of √380?

a)

18.5

b)

19

c)

19.5

d)

20

Pythagorean Theorem Review

Total questions: 80

Worksheet time: 6hrs 30mins

Similar Resources on Wayground