The Pythagorean Theorem states that in a right-angled triangle, 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 other words, if a and b are the lengths of the two shorter sides and c is the length of the hypotenuse, then a² + b² = c². This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery. It is a fundamental concept in geometry and is used to solve many mathematical problems involving right-angled triangles. The Pythagorean Theorem has many applications in real life, such as in architecture, engineering, and physics. For example, it can be used to calculate distances, determine the lengths of sides in a triangle, or even check if a triangle is a right-angled triangle. Understanding the Pythagorean Theorem is essential for anyone studying mathematics, and it is a key concept that can help in solving various problems in geometry and trigonometry.