Pythagorean Theorem: Interactive Quizzes and Practice Questions

Question 1

Which formula represents the Pythagorean Theorem for a right triangle?

Accepted Answer

a^2 + b^2 = c^2

Answer

a^2 - b^2 = c^2

Answer

a + b = c

Question 2

Can the Pythagorean Theorem be used to calculate the distance between two points on a coordinate plane?

Accepted Answer

Yes

Answer

No

Question 3

Which of the following is the converse of the Pythagorean Theorem?

Accepted Answer

If a triangle is a right triangle, then its side lengths satisfy the Pythagorean Theorem.

Answer

If a triangle has side lengths that satisfy the Pythagorean Theorem, then it is a right triangle.

Answer

If a triangle has a hypotenuse, then it is a right triangle.

Answer

If a triangle has a right angle, then its side lengths satisfy the Pythagorean Theorem.

Question 4

The Pythagorean Theorem can be applied to find the area of a:

Accepted Answer

Triangle

Answer

Square

Answer

Rectangle

Answer

Circle

Question 5

In a right triangle, the sum of the squares of the two shorter sides is always _______ the square of the hypotenuse.

Accepted Answer

Equal to

Answer

Greater than

Answer

Less than

Answer

Cannot be determined

Question 6

Who is widely recognized for initially discovering the Pythagorean Theorem?

Accepted Answer

Pythagoras

Answer

Euclid

Answer

Archimedes

Answer

Plato

Question 7

Which of the following sets of numbers cannot be the lengths of the sides of a right triangle?

Accepted Answer

8, 15, 17

Answer

3, 4, 5

Answer

5, 12, 13

Answer

7, 24, 25

Question 8

Which of the following represents the Pythagorean Theorem?

Accepted Answer

a^2 + b^2 = c^2

Answer

a^2 - b^2 = c^2

Answer

a^2 + c^2 = b^2

Answer

a^2 - c^2 = b^2

Question 9

Which of the following represents the Pythagorean Theorem?

Accepted Answer

a^2 + b^2 = c^2

Answer

a + b = c

Answer

a - b = c

Answer

a/b = c

Question 10

If the legs of a right triangle measure 3 units and 4 units, what is the length of the hypotenuse?

Accepted Answer

7 units

Answer

5 units

Answer

12 units

Answer

25 units

Question 11

Which of the following triangles cannot be a right triangle?

Accepted Answer

A triangle with sides 2, 2, and √8

Answer

A triangle with sides 3, 4, and 5

Answer

A triangle with sides 1, 2, and 3

Answer

A triangle with angles 90°, 45°, and 45°

Question 12

If the Pythagorean Theorem is true for a triangle, what type of triangle is it?

Accepted Answer

Right triangle

Answer

Acute triangle

Answer

Obtuse triangle

Answer

Equilateral triangle

Question 13

Which of these is NOT a Pythagorean triple?

Accepted Answer

(9, 10, 17)

Answer

(3, 4, 5)

Answer

(5, 12, 13)

Answer

(7, 24, 25)

Question 14

A ladder is leaning against a wall. The bottom of the ladder is 6 feet from the wall and the top of the ladder reaches a height of 8 feet. What is the length of the ladder?

Accepted Answer

14 feet

Answer

10 feet

Answer

12 feet

Answer

16 feet

Question 15

Which of the following expressions is equivalent to the square root of (a^2 + b^2)?

Accepted Answer

c

Answer

a + b

Answer

a^2 - b^2

Answer

2 * c

Question 16

Which theorem is closely related to the Pythagorean Theorem?

Accepted Answer

Law of Cosines

Answer

Law of Sines

Answer

Triangle Inequality Theorem

Answer

Distance Formula

Question 17

In a right triangle, the hypotenuse is always:

Accepted Answer

Longer than the other two sides

Answer

Shorter than the other two sides

Answer

Equal in length to the other two sides

Answer

Not related to the other two sides

Question 18

What is the main purpose of the Pythagorean Theorem?

Accepted Answer

Finding the length of the sides of a triangle

Answer

Finding the area of a triangle

Answer

Finding the perimeter of a triangle

Answer

Finding the angle measures of a triangle

Question 19

Which mathematical theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides?

Accepted Answer

Pythagorean Theorem

Answer

Sine Theorem

Answer

Cosine Theorem

Answer

Tangent Theorem

Question 20

Which of the following equations represents the Pythagorean Theorem for a triangle with legs of length 'a' and 'b' and a hypotenuse of length 'c'?

Accepted Answer

a^2 + b^2 = c^2

Answer

c^2 - a^2 = b^2

Answer

a + b = c

Answer

a/b = c

Question 21

A ladder is leaning against a wall. The bottom of the ladder is 5 feet from the wall, and the top of the ladder reaches a height of 8 feet. What is the length of the ladder?

Accepted Answer

13 feet

Answer

10 feet

Answer

15 feet

Answer

18 feet

Question 22

In a right triangle, the hypotenuse measures 10 cm and one leg measures 6 cm. What is the length of the other leg?

Accepted Answer

8 cm

Answer

4 cm

Answer

6 cm

Answer

10 cm

Question 23

What geometric shape can you use the Pythagorean Theorem to find the area of?

Accepted Answer

Right triangle

Answer

Isosceles triangle

Answer

Equilateral triangle

Answer

All triangles

Question 24

To which type of triangle is the Pythagorean Theorem applicable?

Accepted Answer

Right triangles

Answer

Isosceles triangles

Answer

Equilateral triangles

Answer

All triangles

Question 25

In a right triangle, the hypotenuse measures 10 units and one leg measures 6 units. What is the length of the other leg, according to the Pythagorean Theorem?

Accepted Answer

8 units

Answer

4 units

Answer

12 units

Answer

16 units

Question 26

In a right triangle, which side is always the longest?

Accepted Answer

Hypotenuse

Answer

Leg

Answer

Base

Question 27

A right triangle has legs of length 3 cm and 4 cm. What is the length of the hypotenuse?

Accepted Answer

7 cm

Answer

5 cm

Answer

12 cm

Answer

25 cm

Question 28

Which of the following numbers cannot be the length of a side of a right triangle?

Accepted Answer

4.5

Answer

1

Answer

2

Answer

3

Question 29

Which of the following sets of numbers forms a Pythagorean triple?

Accepted Answer

(3, 4, 5)

Answer

(4, 5, 6)

Answer

(5, 6, 7)

Answer

(6, 7, 8)

Question 30

In a right triangle, which side's length squared is equal to the sum of the squares of the lengths of the other two sides?

Accepted Answer

Hypotenuse

Answer

Perpendicular

Answer

Base

Question 31

If the length of the hypotenuse of a right triangle is 10 cm and the length of one leg is 6 cm, what is the length of the other leg?

Accepted Answer

8 cm

Answer

4 cm

Answer

16 cm

Question 32

Which of the following is NOT a Pythagorean triple?

Accepted Answer

(5, 12, 13)

Answer

(3, 4, 5)

Answer

(6, 8, 10)

Question 33

The Pythagorean Theorem can be used to find the distance between two points in a coordinate plane.

Accepted Answer

True

Answer

False

Question 34

If the length of the hypotenuse of a right triangle is x and the lengths of the legs are y and z, which of the following equations represents the Pythagorean Theorem?

Accepted Answer

x^2 = y^2 + z^2

Answer

x = y + z

Answer

x = y - z

Question 35

A ladder is leaning against a wall. The bottom of the ladder is 6 feet from the wall and the top of the ladder reaches a height of 8 feet on the wall. How long is the ladder?

Accepted Answer

14 feet

Answer

10 feet

Answer

24 feet

Question 36

Which of the following does NOT represent the Pythagorean Theorem?

Accepted Answer

a^2 = b^2 - c^2

Answer

a^2 + b^2 = c^2

Answer

a + b = c

Question 37

Which of the following is the converse of the Pythagorean Theorem?

Accepted Answer

If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

Answer

If a triangle has three equal sides, then it is a right triangle.

Answer

If a triangle has two sides of equal length, then it is a right triangle.

Question 38

Which of the following is a Pythagorean Theorem formula?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

a + b = c

Answer

a³ + b³ = c³

Question 39

In a right triangle, the square of the length of which side is equal to the sum of the squares of the lengths of the other two sides?

Accepted Answer

Hypotenuse

Answer

Leg 2

Answer

Leg 1

Question 40

Which of the following formulas is the Pythagorean Theorem?

Accepted Answer

a² + b² = c²

Answer

c² - a² = b²

Answer

a² - c² = b²

Answer

b² - c² = a²

Question 41

The Pythagorean Theorem can be applied to which type of triangle?

Accepted Answer

Right triangle

Answer

Acute triangle

Answer

Equilateral triangle

Answer

Obtuse triangle

Question 42

Which trigonometric identity is related to the Pythagorean Theorem?

Accepted Answer

sin²x + cos²x = 1

Answer

cot²x + 1 = csc²x

Answer

csc²x - 1 = cot²x

Answer

tan²x - 1 = sec²x

Question 43

Who is credited with discovering the Pythagorean Theorem?

Accepted Answer

Pythagoras

Answer

Archimedes

Answer

Hypatia

Answer

Euclid

Question 44

Which of the following is NOT a practical application of the Pythagorean Theorem?

Accepted Answer

Predicting the weather

Answer

Calculating the distance across a river

Answer

Determining the length of a ladder

Question 45

A ladder is leaning against a wall. The base of the ladder is 5 feet away from the wall, and the ladder reaches 12 feet up the wall. How long is the ladder?

Accepted Answer

13 feet

Answer

17 feet

Answer

10 feet

Answer

7 feet

Question 46

Which set of side lengths could form a right triangle?

Accepted Answer

5, 12, 13

Answer

2, 3, 4

Answer

4, 5, 6

Answer

7, 7, 10

Question 47

A square has a diagonal of length 10 meters. What is the area of the square?

Accepted Answer

50 square meters

Answer

25 square meters

Answer

100 square meters

Question 48

Two friends walk in perpendicular directions. One friend walks 15 meters east, and the other walks 20 meters north. What is the shortest distance between them?

Accepted Answer

25 meters

Answer

35 meters

Answer

5 meters

Answer

40 meters

Question 49

If the length of each leg of a right triangle is doubled, what happens to the length of the hypotenuse?

Accepted Answer

It is doubled

Answer

It is tripled

Answer

It is quadrupled

Answer

It stays the same

Question 50

Which of the following is NOT a Pythagorean triple?

Accepted Answer

5, 7, 9

Answer

8, 15, 17

Answer

7, 24, 25

Answer

3, 4, 5

Question 51

A rectangular garden measures 12 meters by 16 meters. What is the length of the diagonal path across the garden?

Accepted Answer

20 meters

Answer

28 meters

Answer

4 meters

Answer

192 meters

Question 52

A right triangle has a hypotenuse of 17 cm and one leg of 8 cm. What is the length of the other leg?

Accepted Answer

15 cm

Answer

9 cm

Answer

25 cm

Answer

21 cm

Question 53

What is the square of the hypotenuse equal to in a right triangle?

Accepted Answer

The sum of the squares of the other two sides

Answer

The product of the other two sides

Answer

The difference of the squares of the other two sides