Pythagorean Theorem Review Quiz

What is the formula to find the length of the hypotenuse in a right-angled triangle?

• a + b = c

• 2a + 2b = c

• a^2 + b^2 = c^2

• a^2 - b^2 = c^2

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

• 7

• 12

• 15

• 10

In a right-angled triangle, if the lengths of two legs are 3 and 4, what is the length of the hypotenuse?

• 10

• 7

• 2

• 5

How can the Pythagorean theorem be used to find the diagonal of a square with side length 6?

• The diagonal of the square with side length 6 can be found using the formula: diagonal = √(6^2 + 6^2) = √(36 + 36) = √72 ≈ 8.49

• diagonal = 6 + 6 = 12

• diagonal = 6 - 6 = 0

• diagonal = 6 x 6 = 36

A ladder is leaning against a wall. If the ladder is 10 feet long and the base is 6 feet away from the wall, how high up the wall does the ladder reach?

• The ladder reaches 15 feet up the wall.

• The ladder reaches 8 feet up the wall.

• The ladder reaches 12 feet up the wall.

• The ladder reaches 5 feet up the wall.

What is the converse of the Pythagorean theorem?

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

• The Pythagorean theorem only applies to isosceles triangles

• The Pythagorean theorem only applies to equilateral triangles

• The square of the length of the longest side of a triangle is not equal to the sum of the squares of the other two sides

If the lengths of three sides of a triangle satisfy the Pythagorean theorem, is the triangle a right-angled triangle? (True/False)

• Not sure

• False

• Maybe

• True

In a right-angled triangle, if the lengths of two legs are 8 and 15, what is the length of the hypotenuse?

• 17

• 20

• 25

• 10

A rectangular garden has dimensions 12 feet by 16 feet. What is the length of the diagonal from one corner of the garden to the opposite corner?

• 20 feet

• 28 feet

• 10 feet

• 15 feet

If a triangle has sides of length 5, 12, and 13, does it satisfy the Pythagorean theorem? (True/False)

• Not sure

• True

• False

• Maybe