What theorem is represented by the equation a² + b² = c²?

The equation a² + b² = c² represents the Pythagorean Theorem, which is fundamental in geometry. This theorem describes the relationship between the sides of a right triangle, where 'c' is the length of the hypotenuse (the side opposite the right angle) and 'a' and 'b' are the lengths of the other two sides. This relationship states that the sum of the squares of the lengths of the two shorter sides equals the square of the length of the hypotenuse.

The significance of this theorem lies in its various applications, such as calculating the distance between points in a coordinate system or determining side lengths in construction and navigation. The familiarity with this theorem is essential for students as it lays the foundation for more advanced topics in mathematics, including trigonometry and calculus.