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

To find the length of the hypotenuse (c) in a right triangle, use the formula: c = √(a² + b²).

Front

If one side of a right triangle is 10 and the other side is 12, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 15.6, calculated as c = √(10² + 12²) = √(100 + 144) = √244 ≈ 15.6.

Front

True or False: To find the hypotenuse, you add a² and b², then take the square root.

Back

True.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance formula between two points (x₁, y₁) and (x₂, y₂) is: d = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

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

Back

The length of the hypotenuse is 10, calculated as c = √(8² + 6²) = √(64 + 36) = √100 = 10.

Front

What is a right triangle?

Back

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

Front

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

Back

The length of the other leg is 12, calculated as b = √(c² - a²) = √(13² - 5²) = √(169 - 25) = √144 = 12.

Front

What does 'c' represent in the Pythagorean Theorem?

Back

'c' represents the length of the hypotenuse in a right triangle.

Front

What do 'a' and 'b' represent in the Pythagorean Theorem?

Back

'a' and 'b' represent the lengths of the two legs of a right triangle.