What is the relationship between the sides of a right triangle according to the Pythagorean theorem?

The Pythagorean theorem establishes a fundamental relationship between the lengths of the sides in a right triangle. Specifically, it states that the sum of the squares of the lengths of the two legs (denoted as a and b) is equal to the square of the length of the hypotenuse (denoted as c). This relationship is expressed mathematically as a² + b² = c².

In this context, the hypotenuse is the side opposite the right angle and is always the longest side of the triangle. The theorem is applicable only to right triangles and plays a crucial role in various aspects of geometry, such as determining distances and verifying triangle congruence.

Other relationships listed do not correctly express the relationship defined by the Pythagorean theorem. For instance, the equation a + b = c does not account for the squared terms, nor does it imply a relationship that holds in right triangles. Thus, the correct choice that accurately represents the Pythagorean theorem is that a² + b² equals c², where c is indeed the hypotenuse.