Which theorem states that a² + b² = c²?

The Pythagorean theorem is a fundamental principle in geometry that establishes a relationship in right triangles. It states that the sum of the squares of the lengths of the legs (a and b) is equal to the square of the length of the hypotenuse (c). This relationship is expressed mathematically as (a² + b² = c²).

This theorem is crucial for various applications in mathematics, science, and engineering, providing a method to determine distances, angles, and for solving real-world problems involving right triangles. It is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.

The other options, while important in their own right within mathematics, pertain to different concepts. The triangle inequality theorem describes the relationship between the lengths of sides of a triangle and does not specifically provide any formula like the Pythagorean theorem. The congruency theorem addresses the conditions under which two triangles can be considered congruent, but does not involve the relationship between the sides and angles. The hypotenuse theorem is often used as a colloquial reference to the Pythagorean theorem but is not the formal name recognized in mathematical literature.