In a right triangle, what does the Pythagorean theorem state?

The Pythagorean theorem is a fundamental principle in geometry that applies specifically to right triangles. It states that 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. In mathematical terms, if we denote the lengths of the two legs of the triangle as 'a' and 'b,' and the length of the hypotenuse as 'c,' the relationship can be formulated as a² + b² = c².

This relationship allows us to determine the length of any one side of a right triangle if the lengths of the other two sides are known, making it a vital tool in various applications, such as architecture, engineering, and many fields of science. The theorem is essential in calculating distances and angles and has numerous practical uses in real-world scenarios.

The other choices do not reflect the correct relationship defined by the Pythagorean theorem, focusing either on incorrect formulations or operations that do not apply to right triangles.