What is the Pythagorean Theorem?

The Pythagorean Theorem is a fundamental principle in geometry that establishes a 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, denoted as c) is equal to the sum of the squares of the lengths of the other two sides (often referred to as a and b). This is concisely expressed as ( a^2 + b^2 = c^2 ).

This relationship is profoundly useful in various applications, including determining the distance between points in a coordinate plane, solving real-world problems involving right triangles, and providing a foundation for more advanced mathematical concepts. The Pythagorean Theorem is critical in fields such as architecture, engineering, and physics, where dimensions and spatial relationships are essential.

The other options do not represent the Pythagorean Theorem. The second option suggests a simple arithmetic relationship without regard to the nature of the triangle. The third option implies averaging sides, which does not apply in the context of right triangles. The fourth option presents a difference of squares, which is unrelated to the right triangle's properties. Thus, the correct choice effectively captures the essence of the