Question 1

Which of the following best describes the Pythagorean Theorem?

Accepted Answer

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Answer

The area of a triangle is half the base times the height.

Answer

The sum of the sides of a triangle is equal to the perimeter.

Answer

In any triangle, the sum of the angles is 180°.

Question 2

If a right triangle has legs of lengths 6 and 8, what is the length of the hypotenuse?

Accepted Answer

10

Answer

12

Answer

14

Answer

16

Question 3

Which of the following sets of numbers can be the sides of a right triangle?

Accepted Answer

5, 12, 13

Answer

9, 12, 15

Answer

7, 24, 26

Answer

8, 15, 20

Question 4

In a right triangle, if one leg is 9 and the hypotenuse is 15, what is the length of the other leg?

Accepted Answer

12

Answer

10

Answer

11

Answer

13

Question 5

What is the area of a square with side length equal to the hypotenuse of a right triangle with legs 3 and 4?

Accepted Answer

25

Answer

16

Answer

36

Answer

9

Question 6

Which of the following is NOT a Pythagorean triple?

Accepted Answer

6, 8, 11

Answer

5, 12, 13

Answer

3, 4, 5

Answer

8, 15, 17

Question 7

If a right triangle has a hypotenuse of 13 and one leg of 5, what is the length of the other leg?

Accepted Answer

12

Answer

9

Answer

10

Answer

11

Question 8

Which of the following statements is true about the hypotenuse in a right triangle?

Accepted Answer

It is always opposite the right angle.

Answer

It is always equal to one of the legs.

Answer

It is always adjacent to the right angle.

Answer

It is always the shortest side.

Question 9

If the sides of a right triangle are 7, 24, and 25, which side is the hypotenuse?

Accepted Answer

25

Answer

24

Answer

None of these

Answer

7

Question 10

How can you verify if a triangle with sides 9, 12, and 15 is a right triangle?

Accepted Answer

Check if 9² + 12² = 15²

Answer

Check if 9² = 12² + 15²

Answer

Check if 9 + 12 + 15 = 36

Answer

Check if 9 + 12 = 15

Question 11

What is the length of the hypotenuse of a right triangle with legs 8 and 15?

Accepted Answer

17

Answer

20

Answer

18

Answer

19

Question 12

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

Accepted Answer

8

Answer

5

Answer

9

Answer

7

Question 13

Which of the following is a correct application of the Pythagorean Theorem?

Accepted Answer

Determining the length of a missing side in a right triangle

Answer

Calculating the area of a rectangle

Answer

Finding the perimeter of a triangle

Answer

Measuring the angles of a triangle

Question 14

If a triangle has sides 8, 15, and 17, is it a right triangle?

Accepted Answer

Yes

Answer

Only if 8 is the hypotenuse

Answer

No

Answer

Only if 17 is the hypotenuse

Question 15

Which of the following is NOT a property of the hypotenuse in a right triangle?

Accepted Answer

It is always equal to one of the legs.

Answer

It is the longest side.

Answer

It is used in the Pythagorean Theorem.

Answer

It is opposite the right angle.

Question 16

If a right triangle has legs of lengths 5 and 12, what is the length of the hypotenuse?

Accepted Answer

13

Answer

14

Answer

15

Answer

16

Question 17

Which of the following is a Pythagorean triple?

Accepted Answer

6, 8, 10

Answer

9, 11, 14

Answer

7, 10, 12

Answer

5, 7, 9

Question 18

In a right triangle, if one leg is 8 and the hypotenuse is 10, what is the length of the other leg?

Accepted Answer

6

Answer

5

Answer

9

Answer

7

Question 19

Which of the following can be used to prove the Pythagorean Theorem?

Accepted Answer

Both A and B

Answer

Neither A nor B

Answer

Geometric representation

Answer

Algebraic manipulation

Question 20

If a right triangle has a hypotenuse of 26 and one leg of 24, what is the length of the other leg?

Accepted Answer

10

Answer

14

Answer

12

Answer

16

Question 21

In a right triangle, if the legs have lengths of 5 and 12, what is the length of the hypotenuse?

Accepted Answer

13

Answer

√169

Answer

17

Answer

∛169

Question 22

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

Accepted Answer

All of the above

Answer

3, 4, 5

Answer

5, 12, 13

Answer

8, 15, 17

Question 23

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

Accepted Answer

8

Answer

4

Answer

8²

Answer

√64

Question 24

In a right triangle with hypotenuse 25 and one leg 24, what is the area of the triangle?

Accepted Answer

84 square units

Answer

140 square units

Answer

168 square units

Answer

70 square units

Question 25

Which equation represents the Pythagorean theorem?

Accepted Answer

a² + b² = c²

Answer

(a + b)² = c²

Answer

a² + b² = c

Answer

a + b = c²

Question 26

A ladder 13 feet long leans against a vertical wall. If the bottom of the ladder is 5 feet from the wall, how high up the wall does the ladder reach?

Accepted Answer

12 feet

Answer

8 feet

Answer

√144 feet

Answer

144 feet

Question 27

In a right triangle, if a² = 49 and b² = 144, what is the value of c?

Accepted Answer

17

Answer

19

Answer

15

Answer

13

Question 28

Which of the following is NOT a valid right triangle?

Accepted Answer

9-12-15

Answer

8-15-17

Answer

3-4-5

Answer

5-12-13

Question 29

If the diagonal of a rectangle is 10 units and one side is 6 units, what is the length of the other side?

Accepted Answer

8 units

Answer

√64 units

Answer

4 units

Answer

64 units

Question 30

In an isosceles right triangle, what is the ratio of a leg to the hypotenuse?

Accepted Answer

1:√2

Answer

1:2

Answer

√2:2

Answer

1:√3

Question 31

A 24-foot wire is stretched between the top of a 20-foot pole and a point on the ground. How far is the point on the ground from the base of the pole?

Accepted Answer

14 feet

Answer

16 feet

Answer

12 feet

Answer

8 feet

Question 32

If the legs of a right triangle are in the ratio 3:4 and the hypotenuse is 25, what is the length of the shorter leg?

Accepted Answer

15

Answer

9

Answer

12

Answer

20

Question 33

Which of the following is true for any right triangle?

Accepted Answer

The square of the hypotenuse equals the sum of squares of the other two sides

Answer

The sum of the lengths of all sides is always even

Answer

The hypotenuse is always twice the length of the shortest side

Answer

The longest side is always more than twice the length of the shortest side

Question 34

In a 3-4-5 right triangle, what is the sine of the smallest angle?

Accepted Answer

3/5

Answer

5/4

Answer

4/5

Answer

5/3

Question 35

If the area of a right triangle is 30 square units and one of its legs is 12 units, what is the length of the hypotenuse?

Accepted Answer

13 units

Answer

17 units

Answer

√169 units

Answer

15 units

Question 36

A square has a diagonal of length 10√2. What is the area of the square?

Accepted Answer

200 square units

Answer

400 square units

Answer

100 square units

Answer

50 square units

Question 37

If the legs of a right triangle are x and y, and the hypotenuse is z, which of the following is NOT a valid Pythagorean triple?

Accepted Answer

x = 9, y = 40, z = 41

Answer

x = 3, y = 4, z = 5

Answer

x = 7, y = 24, z = 25

Answer

x = 5, y = 12, z = 13

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