What is the formula represented in the Pythagorean theorem?

The Pythagorean theorem is a fundamental principle in geometry that describes the relationship between the sides of a right triangle. The correct formula, ( a^2 + b^2 = c^2 ), states that the sum of the squares of the two legs (the sides forming the right angle, represented as ( a ) and ( b )) is equal to the square of the hypotenuse (the side opposite the right angle, represented as ( c )). This theorem is crucial in various mathematical applications, including solving for unknown side lengths in right triangles, and it establishes the foundational relationship among the sides.

In contrast, other options do not accurately represent this relationship. The option indicating ( a + b = c ) misrepresents the geometric principles by suggesting that the lengths of the sides can simply be added to yield the hypotenuse, which is not true in right triangles. Furthermore, the equation ( c = a + b ) suggests a linear relationship rather than a quadratic one, which does not hold for triangles. Lastly, ( c^2 = a + b ) incorrectly implies that the square of the hypotenuse is equivalent to the sum of the lengths of the other two sides, which contradicts the