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 are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle. They are usually referred to as 'a' and 'b' in the Pythagorean Theorem.

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle. It is denoted as 'c' in the Pythagorean Theorem.

Front

If one leg of a right triangle is 15 cm and the hypotenuse is 21 cm, what is the length of the other leg?

Back

Using the Pythagorean Theorem: 15² + b² = 21²; b² = 21² - 15²; b² = 441 - 225; b² = 216; b = √216 ≈ 14.7 cm.

Front

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

Back

True.

Front

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

Back

c = √(a² + b²), where 'c' is the hypotenuse and 'a' and 'b' are the legs.

Front

What is the formula to find the length of a leg if the hypotenuse and the other leg are known?

Back

a = √(c² - b²) or b = √(c² - a²), where 'c' is the hypotenuse and 'a' and 'b' are the legs.

Front

Find the length of the missing side if one leg is 9 and the hypotenuse is 15.

Back

Using the Pythagorean Theorem: 9² + b² = 15²; b² = 15² - 9²; b² = 225 - 81; b² = 144; b = √144 = 12.

Front

If the lengths of the legs of a right triangle are 8 cm and 6 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(8² + 6²); c = √(64 + 36); c = √100; c = 10 cm.

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 lengths of the legs equals the square of the length of the hypotenuse.