What does the Pythagorean Theorem state?

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the two legs (the sides that form the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle). This relationship is mathematically represented as a squared plus b squared equals c squared, 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 because it provides a method to calculate the length of any one of the three sides if the lengths of the other two are known. It is widely applicable in various fields such as physics, engineering, and architecture. The statement captures the essence of the relationship between the sides of a right triangle, making it a critical concept in mathematics.