What does the Pythagorean theorem state about the sides of a right triangle?

The Pythagorean theorem 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 succinctly expressed as a² + b² = c², where a and b represent the lengths of the legs of the triangle, and c represents the length of the hypotenuse. This theorem is fundamental in geometry and is widely used to calculate distances and solve problems involving right triangles.

The other options do not accurately describe the relationship between the sides of a right triangle. The second option, which sums the lengths of the sides, fails to recognize the crucial aspect of squaring the lengths. The third option incorrectly suggests a subtractive relationship, which does not hold true in right triangles. Lastly, the fourth option simply provides the perimeter formula (2a + 2b = 2c) without addressing the specific relationship central to the Pythagorean theorem.