Basic algebra is a fundamental branch of mathematics that focuses on the use of symbols and numbers to represent relationships and solve problems. It introduces concepts such as variables, expressions, equations, and inequalities, allowing for the manipulation of mathematical statements. Algebra is essential for solving real-world problems in fields like science, engineering, and business, as it helps model situations and find unknown values. Techniques such as simplification, factoring, and graphing equations provide a strong foundation for advanced mathematical studies. The Pythagorean theorem is a key principle in geometry that describes the relationship between the three sides of a right triangle. Expressed as π 2 + π 2 = π 2 , the theorem states that the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse). This theorem is widely used in various real-world applications, such as navigation, construction, and physics, where precise calculations of distances and measurements are required. Understanding how to apply the theorem helps in problem-solving scenarios involving right-angled triangles.