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 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 a right triangle has legs of lengths 3 cm and 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

Can the lengths 20, 25, and 15 form a right triangle?

Back

Yes, they can form a right triangle because 20² + 15² = 400 + 225 = 625 = 25².

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

Is the statement 'a² + b³ = c⁴' correct for the Pythagorean Theorem?

Back

No, the correct statement is 'a² + b² = c²'.

Front

What is a right triangle?

Back

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

Front

If one leg of a right triangle is 12 cm and the hypotenuse is 13 cm, what is the length of the other leg?

Back

The length of the other leg is 5 cm, calculated as: b = √(c² - a²) = √(13² - 12²) = √(169 - 144) = √25 = 5.

Front

True or False: You can find right triangles when they build houses.

Back

True.

Front

What is the Pythagorean triplet?

Back

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