The Pythagorean Theorem states that in a right-angled triangle (a triangle with one angle of 90 degrees), the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This can be written as a mathematical equation: a² + b² = c², where a and b are the lengths of the two shorter sides, and c is the length of the hypotenuse.