Free Printable Pythagorean Theorem and Distance Formula

1.

What is the equation for the Pythagorean Theorem?

a)

$a^2+b^2=c^2$

b)

$a+b=c$

c)

$a+b+c$

d)

$a-b^2=c$

2.

What do the lengths a and b represent in the Pythagorean Theorem?

a)

Legs

b)

Hypotenuse

3.

The hypotenuse is which of the following?

a)

the shortest side

b)

the middle side

c)

the longest side

4.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

5.

What is the opposite of squaring a number?

a)

divide

b)

multiply

c)

fractions

d)

square root

6.

What is the term for 3 whole numbers that satisfy the Pythagorean Theorem?

a)

Pythagorean Triple

b)

Pythagorean Duo

c)

Pythagorean Double

d)

Pythagorean Converse

7.

Which of the following is NOT a Pythagorean Triple?

a)

3, 4, 5

b)

5, 12, 13

c)

7, 15, 20

d)

12, 16, 20

8.

What do we use to determine if 3 given side lengths make a right triangle?

a)

Pythagorean Triple

b)

Pythagorean Double

c)

Pythagorean Duo

d)

Pythagorean Converse

9.

Which side length represents the hypotenuse?

a)

5

b)

12

c)

13

d)

None of these

10.

Find the missing side:

a)

7

b)

17

c)

18.2

d)

22

11.

Find the missing side:

a)

20.4

b)

26.5

c)

30.1

d)

14.2

12.

Given the side lengths a=12 and c=20, find b.

a)

14.2

b)

16

c)

8

d)

14

13.

Do the following side lengths make a right triangle?

$2,\ 4,\ \sqrt{20}$

a)

Yes

b)

No

14.

Which of the following makes a right triangle?

a)

3, 5, 8

b)

1, 2, 3

c)

$2,\ 3,\ \sqrt{13}$

d)

$10,\ 20,\ \sqrt{30}$

15.

What is the equation for the Distance Formula?

a)

$d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

b)

$d\ =\ x\ -\ y$

c)

$d^2=a+b$

d)

$d=\sqrt{x^2-y^2}$

16.

Which is the correct way to find the distance between the points (5,2) and (0,1)?

a)

$d=5^2+2^2$

b)

$d=\sqrt{\left(5-0\right)^2+\left(2-1\right)^2}$

c)

$d=7+1$

d)

$d=\sqrt{5^2-2^2}$

17.

Find the distance between the points (8,6) and (16,0).

a)

10

b)

5

c)

100

d)

12

18.

Find the distance between the points (-3,0) and (0,4)

a)

5

b)

6

c)

7

d)

8

19.

Find the distance between (2,6) and (9,3)

a)

5.9

b)

7.6

c)

8.4

d)

6.7

20.

60 miles east of Wichita is Eureka.

30 miles south of Wichita is Wellington.

How far apart are Eureka and Wellington?

(Round to the nearest WHOLE number.)

(a)

21.

When finding the diagonal between two corners of a cube, what formula do you use?

a)

$l^2+w^2+h^2=d^2$

b)

$c=\sqrt{lwh}$

c)

$d=lwh$

d)

$a^2+b^2=c^2$

22.

Find the distance from corner to corner.

(a)

23.

a)

9.4

b)

11.4

c)

13.5

d)

15.2

24.

What is the distance between two opposite corners of a rectangular prism that has a length of 8, and width of 3, and a height of 11?

a)

11.6

b)

9

c)

12

d)

13.9

25.

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

26.

The slide at the playground has a height of 6 feet. The base of the slide measured on the ground is 8 feet. What is the length of the slide?

a)

8 feet

b)

5.29 feet

c)

10 feet

d)

14 feet

27.

Your family wants to purchase a new laptop with a 17" screen. Since the 17 inches represents the diagonal measurement of the screen (upper corner to lower corner), you want to find out the actual dimensions of the laptop. When you measured the laptop at the store, the width was 10 inches, but you don't remember the height. Calculate the height of the laptop to the nearest tenth of an inch.

a)

7 inches

b)

10 inches

c)

19.7 inches

d)

13.7 inches

28.

What is the length of the missing side? *NOTE: side lengths of 10 and 12.

a)

15.6

b)

6.6

c)

44

d)

16

29.

What is the height of the cone?

a)

14 cm

b)

8 cm

c)

12 cm

d)

13.9 cm

30.

An ant and a fly want to race to the opposite corner of a cube with side lengths of 7ft. What is the total distance traveled for both insects? (Select 2 answers!)

a)

The fly travels 12.1 ft.

b)

The fly travels 16.2 ft.

c)

The ant travels 16.9ft.

d)

The ant travels 9.1 ft

Pythagorean Theorem and Distance Formula

Total questions: 30

Worksheet time: 2hrs 42mins

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