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

Back

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

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 length of the hypotenuse is 5 cm, calculated as: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the square root of a number?

Back

The square root of a number x is a value that, when multiplied by itself, gives x. For example, √9 = 3 because 3 × 3 = 9.

Front

What is the opposite of squaring a number?

Back

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

Front

In a right triangle, if one side is 6 cm and the hypotenuse is 10 cm, what is the length of the other side?

Back

The length of the other side is 8 cm, calculated as: b = √(10² - 6²) = √(100 - 36) = √64 = 8.

Front

What does it mean to find the missing side of a right triangle?

Back

Finding the missing side of a right triangle involves using the Pythagorean Theorem to calculate the length of one side when the lengths of the other two sides are known.

Front

What is the relationship between the areas of the squares on the sides of a right triangle?

Back

The sum of the areas of the two smaller squares (on the legs) is equal to the area of the larger square (on the hypotenuse).

Front

If a ladder is placed 10 feet away from a wall and reaches a height of 24 feet, how long is the ladder?

Back

The length of the ladder is 26 feet, calculated as: c = √(10² + 24²) = √(100 + 576) = √676 = 26.

Front

What is a right triangle?

Back

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