Which equation represents the Pythagorean theorem?

The equation that represents the Pythagorean theorem is expressed as ( a^2 + b^2 = c^2 ). This theorem is a fundamental principle in geometry that applies to right-angled triangles. In this equation, ( a ) and ( b ) represent the lengths of the legs of the triangle, while ( c ) represents the length of the hypotenuse, which is the side opposite the right angle.

This relationship shows that the sum of the squares of the two shorter sides equals the square of the longest side. This theorem is crucial in various applications, including architecture, engineering, and physics, as it provides a method to determine the distance between points in a plane and helps in solving problems that involve right triangles.

The other equations provided do not correctly represent the relationship defined by the Pythagorean theorem. They involve different mathematical principles that do not apply to the specific context of right triangles.