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 is expressed as: a² + b² = c².

Front

Which type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Front

If a right triangle has side lengths of 6, 8, and 10, which side is the hypotenuse?

Back

The hypotenuse is 10.

Front

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

Back

The formula is c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.

Front

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

Back

The hypotenuse is 5 cm, calculated as √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

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

Back

False. The Pythagorean Theorem can only be used for right triangles.

Front

In a right triangle, if the lengths of the two legs are 5 cm and 12 cm, what is the length of the hypotenuse?

Back

The hypotenuse is 13 cm, calculated as √(5² + 12²) = √(25 + 144) = √169 = 13.

Front

What is the relationship between the sides of a right triangle according to the Pythagorean Theorem?

Back

The sum of the squares of the two shorter sides (legs) equals the square of the longest side (hypotenuse).

Front

If a right triangle has a hypotenuse of 15 cm and one leg of 9 cm, what is the length of the other leg?

Back

The length of the other leg is 12 cm, calculated as √(15² - 9²) = √(225 - 81) = √144 = 12.

Front

What is the Pythagorean triple?

Back

A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². An example is (3, 4, 5).