Pythagorean Theorem Quiz

What is the Pythagorean theorem?

• The Pythagorean theorem states that in a right-angled triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides.

• The Pythagorean theorem states that in a right-angled triangle, the length of the hypotenuse is equal to the sum of the lengths of the other two sides.

• The Pythagorean theorem states that in a right-angled 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.

• The Pythagorean theorem states that in a right-angled triangle, the length of one side is equal to the sum of the lengths of the other two sides.

Answer explanation

The Pythagorean theorem states that in a right-angled 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.

In a right triangle, which side is considered as the hypotenuse?

• The side opposite the acute angle

• The side opposite the obtuse angle

• The side opposite the right angle

• The side adjacent to the right angle

Answer explanation

The hypotenuse is the side opposite the right angle in a right triangle.

If the lengths of two sides of a right triangle are 3 and 4, what is the length of the hypotenuse?

• 6

• 8

• 5

• 7

Answer explanation

In a right triangle, the length of the hypotenuse can be found using the Pythagorean theorem. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the lengths of the two sides are 3 and 4. Using the theorem, we can calculate the length of the hypotenuse as √(3^2 + 4^2) = √(9 + 16) = √25 = 5. Therefore, the correct length of the hypotenuse is 5.

What is the formula to calculate the length of the hypotenuse in a right triangle?

• Euclidean theorem

• Pythagorean theorem

• Trigonometric theorem

• Law of Sines

Answer explanation

The formula to calculate the length of the hypotenuse in a right triangle is the Pythagorean theorem.

If the lengths of two sides of a right triangle are 5 and 12, what is the length of the hypotenuse?

• 7

• 10

• 15

• 13

Answer explanation

In a right triangle, the length of the hypotenuse can be found using the Pythagorean theorem. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the lengths of the two sides are 5 and 12. Using the theorem, we can calculate the length of the hypotenuse as √(5^2 + 12^2) = √(25 + 144) = √169 = 13. Therefore, the correct choice is 13.

In a right triangle, if the lengths of two sides are a and b, what is the length of the hypotenuse?

• a + b

• √(a² + b²)

• ab

• a - b

Answer explanation

The length of the hypotenuse in a right triangle with sides of length a and b is given by the formula √(a² + b²). This choice is the correct answer because it represents the Pythagorean theorem.

What is the length of the hypotenuse in a right triangle if the lengths of the other two sides are 6 and 8?

• 10

• 14

• 12

• 16

What is the Pythagorean theorem used for?

• To calculate the area of a triangle

• To calculate the length of the hypotenuse in a right triangle

• To calculate the volume of a sphere

• To calculate the circumference of a circle

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

• 2

• 6

• √14

• √6

What is the Pythagorean theorem used to calculate in a right triangle if the lengths of the hypotenuse and one side are known?

• The length of the other side

• The area of the triangle

• The volume of the triangle

• The circumference of the triangle