The Pythagorean Theorem is a fundamental concept in geometry that states: 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 mathematical terms, if a and b are the lengths of the two shorter sides and c is the length of the hypotenuse, then a^2 + b^2 = c^2. This theorem can be used to calculate the length of any side of a right-angled triangle, as long as the lengths of the other two sides are known. It is also the basis for trigonometry and has many practical applications in fields such as engineering, architecture, and physics. The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery. It is one of the most well-known and widely used mathematical formulas in the world, and its proof has fascinated mathematicians for centuries. Understanding the Pythagorean Theorem is essential for anyone studying geometry or mathematics, as it provides the foundation for many other mathematical concepts and equations. By mastering this simple yet powerful formula, students can unlock a deeper understanding of the relationships between the sides of a right-angled triangle and apply their knowledge to solve a wide range of problems.