What does the Pythagorean theorem state?

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This is mathematically expressed as ( a² + b² = c² ), where ( c ) represents the length of the hypotenuse and ( a ) and ( b ) represent the lengths of the other two sides.

This theorem is fundamental in geometry and is widely used in various applications involving right triangles, such as calculating distances, creating designs in architecture, and solving real-world problems involving right-angled triangles. The relationship described by the theorem allows us to find the length of one side of a triangle when the lengths of the other two sides are known, making it a powerful tool in both theoretical mathematics and practical situations.

The other choices do not accurately represent the Pythagorean theorem, as they either misstate the relationship or present different equations that do not pertain to the properties of right triangles.