What is stated by the Pythagorean theorem?

The Pythagorean theorem specifically relates to right triangles and establishes a fundamental relationship between the lengths of the sides. According to this theorem, 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.

In this context, it’s important to recognize that the theorem only applies to right-angled triangles. The first choice, which suggests a + b = c, does not provide the necessary relationship that exists in right triangles, while the third choice incorrectly implies a relationship involving subtraction of squares. The fourth option provides a statement related to the sum of angles in a triangle, which does not pertain to side lengths at all. Thus, the correct application of the theorem is clearly represented by the choice stating that a² + b² = c², which confirms the geometric principles related to right triangles.