The Pythagorean Theorem is a fundamental concept in mathematics that relates to the lengths of the sides of a right triangle. It states that 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 of a right triangle and c is the length of the hypotenuse, then a^2 + b^2 = c^2. This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery. The Pythagorean Theorem has many practical applications, such as in construction, engineering, and physics, where calculating distances and solving geometric problems are essential. Understanding the Pythagorean Theorem allows us to determine unknown side lengths of right triangles and is the basis for trigonometry, a branch of mathematics that deals with the relationships between the sides and angles of triangles. Overall, the Pythagorean Theorem is a powerful tool that plays a key role in various mathematical disciplines and real-world scenarios. Mastering this concept can greatly enhance one's problem-solving skills and mathematical understanding.