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: a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

If one side of a right triangle is 9 and the other side is 12, what is the length of the hypotenuse?

Back

The hypotenuse is 15. (Using the Pythagorean Theorem: 9² + 12² = c² -> 81 + 144 = c² -> 225 = c² -> c = 15.)

Front

What is the formula to find the length of one side of a right triangle if the other two sides are known?

Back

To find the length of one side, rearrange the Pythagorean Theorem: a = √(c² - b²) or b = √(c² - a²).

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem only applies to right triangles.

Front

If the lengths of the sides of a triangle are 5, 12, and 13, does it form a right triangle?

Back

Yes, it forms a right triangle because 5² + 12² = 13² (25 + 144 = 169).

Front

What is the length of the diagonal of a rectangle with a width of 15 inches and a length of 20 inches?

Back

The diagonal is 25 inches. (Using the Pythagorean Theorem: 15² + 20² = d² -> 225 + 400 = d² -> 625 = d² -> d = 25.)

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

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

Back

The length of the other leg is 8. (Using the Pythagorean Theorem: 6² + b² = 10² -> 36 + b² = 100 -> b² = 64 -> b = 8.)

Front

What is a right triangle?

Back

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