What mathematical equation is known as the Pythagorean Theorem?

The Pythagorean Theorem is a fundamental principle in mathematics that relates to right-angled triangles. It specifically states that in a right triangle, 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. This relationship is expressed mathematically as ( a^2 + b^2 = c^2 ), where ( c ) represents the length of the hypotenuse, and ( a ) and ( b ) represent the lengths of the triangle's two other sides.

This theorem is crucial in various fields such as geometry, physics, engineering, and computer science, influencing how we calculate distances, construct models, and solve real-world problems. Different forms of equations like the ones in other options do not represent this fundamental relationship accurately. For example, the addition and subtraction equations do not convey the specific relationship of squaring the side lengths, which is essential to the Pythagorean Theorem.