What is the Pythagorean theorem?

The Pythagorean theorem is a fundamental principle in geometry that describes the relationship between the lengths of the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle, commonly referred to as c) is equal to the sum of the squares of the lengths of the other two sides (commonly referred to as a and b). This relationship is mathematically expressed as ( a² + b² = c² ).

This equation encapsulates a key concept in geometry and is widely used in various applications, including determining distances in coordinate systems, solving problems involving right triangles, and in real-world contexts such as construction and navigation. The theorem holds true only for right triangles, making it a crucial aspect of Euclidean geometry. Understanding this theorem is essential for students as it lays a foundational understanding of relationships in geometry and paves the way for further exploration into trigonometry and advanced mathematics.