Topic 4 Pythagoras Theorem

Question 1

What is the Pythagorean Theorem formula?

Answer 1

a² + b² = c²

Question 2

In the Pythagorean Theorem, what does ‘c’ represent?

Answer 2

‘c’ represents the length of the hypotenuse.

Question 3

True or False: The Pythagorean Theorem applies only to right-angled triangles.

Answer 3

True

Question 4

What type of triangle can you apply the Pythagorean Theorem to?

Answer 4

Right-angled triangles.

Question 5

If one leg of a right triangle is 3 cm and the other leg is 4 cm, what is the length of the hypotenuse?

Answer 5

5 cm

Question 6

Fill in the blank: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the ______.

Answer 6

other two sides

Question 7

What is the length of a hypotenuse if the legs are 6 cm and 8 cm?

Answer 7

10 cm

Question 8

If a² = 49, what is the value of a?

Answer 8

7

Question 9

What is the first step in using the Pythagorean Theorem?

Answer 9

Identify the lengths of the two legs.

Question 10

Calculate the length of the hypotenuse if the legs are 5 m and 12 m.

Answer 10

13 m

Question 11

True or False: The Pythagorean Theorem can be used for any triangle.

Answer 11

False

Question 12

If c = 13 and a = 5, what is b?

Answer 12

12

Question 13

What do you do if you know the hypotenuse and one leg, and need to find the other leg?

Answer 13

Use the formula b = √(c² - a²).

Question 14

Fill in the blank: The Pythagorean Theorem is named after the ancient Greek mathematician ______.

Answer 14

Pythagoras

Question 15

What is the hypotenuse of a triangle with legs measuring 1 and √3?

Answer 15

2

Question 16

How do you find the length of a leg if you have the hypotenuse and the other leg?

Answer 16

Use the formula a = √(c² - b²).

Question 17

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

Answer 17

Yes

Question 18

What is the relationship between the sides of a right triangle?

Answer 18

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

Question 19

Find the value of c if a = 9 and b = 12.

Answer 19

15

Question 20

If a = 7 and c = 25, what is b?

Answer 20

24

Question 21

True or False: In a right triangle, the hypotenuse is always the longest side.

Answer 21

True

Question 22

What can you conclude if a² + b² < c²?

Answer 22

The triangle is obtuse.

Question 23

What can you conclude if a² + b² > c²?

Answer 23

The triangle is acute.

Question 24

In a 30-60-90 triangle, if the shorter leg is x, what is the length of the hypotenuse?

Answer 24

2x

Question 25

In a 45-45-90 triangle, if the legs are x, what is the length of the hypotenuse?

Answer 25

x√2

Question 26

What is the area of a right triangle with legs of length 6 and 8?

Answer 26

24 square units

Question 27

If a triangle has sides 9, 12, and 15, is it a right triangle?

Answer 27

Yes

Question 28

If c = 10 and b = 6, what is a?

Answer 28

8

Question 29

What does the Pythagorean Theorem help you calculate?

Answer 29

The length of a side in a right triangle.

Question 30

What is the hypotenuse of a right triangle if the legs are 7 cm and 24 cm?

Answer 30

25 cm

Question 31

True or False: The Pythagorean Theorem is only applicable in two dimensions.

Answer 31

True

Question 32

What is the length of one leg if the hypotenuse is 10 and the other leg is 6?

Answer 32

8