Pythagorean Theorem

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: c² = a² + b².

Front

What is the formula to find the length of the hypotenuse?

Back

The formula to find the length of the hypotenuse (c) in a right triangle is: c = √(a² + b²).

Front

If one side of a right triangle is 6 and the other side is 8, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 10. (Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10.)

Front

What is the opposite of squaring a number?

Back

The opposite of squaring a number is taking the square root.

Front

In a right triangle, if one side is 5 and the hypotenuse is 13, what is the length of the other side?

Back

The length of the other side is 12. (Using the Pythagorean Theorem: 13² = 5² + b², so 169 = 25 + b², thus b² = 144, and b = 12.)

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

Back

Yes, it is a right triangle. (Using the Pythagorean Theorem: 25² = 7² + 24², so 625 = 49 + 576, which is true.)

Front

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

Back

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

Front

How do you find the length of a side in a right triangle if you know the hypotenuse and one other side?

Back

You can find the length of the missing side using the formula: a = √(c² - b²) or b = √(c² - a²).

Front

What is the length of the diagonal of a rectangle with a width of 50 yards and a length of 100 yards?

Back

The length of the diagonal is 111.8 yards. (Using the Pythagorean Theorem: d = √(50² + 100²) = √(2500 + 10000) = √12500 = 111.8.)