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

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

Back

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

Front

In a right triangle, which side is the hypotenuse?

Back

The hypotenuse is the side opposite the right angle and is always the longest side.

Front

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

Back

The hypotenuse is 5 meters, calculated using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

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 legs (a and b) equals the square of the hypotenuse (c): a² + b² = c².

Front

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

Back

True.

Front

What is the length of the diagonal of a rectangle that is 90 meters wide and 120 meters long?

Back

The diagonal is 150 meters, calculated using the Pythagorean Theorem: c = √(90² + 120²) = √(8100 + 14400) = √22500 = 150.

Front

What do you call the two shorter sides of a right triangle?

Back

The two shorter sides are called the legs.

Front

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

Back

The other leg is 12 meters, calculated using the Pythagorean Theorem: b = √(c² - a²) = √(13² - 5²) = √(169 - 25) = √144 = 12.

Front

What is the term for the longest side of a right triangle?

Back

The longest side of a right triangle is called the hypotenuse.