The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two other sides. The formula is a2 + b2 = c2, where a and b are the lengths of the two sides adjacent to the right angle, and c is the length of the hypotenuse. The document provides examples of using the Pythagorean theorem to calculate the length of one side of a right triangle when the other two sides are known.