What does the Pythagorean Theorem state?

The Pythagorean Theorem states that in a right-angled 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 a² + b² = c², where 'a' and 'b' are the lengths of the two legs of the triangle, and 'c' is the length of the hypotenuse.

This theorem is fundamental in geometry because it defines the geometric relationship between the three sides of a right triangle. It is extensively applied in various fields, including engineering, physics, and computer science, for determining distances and solving problems involving right triangles.

The other options do not represent the correct relationship for a right triangle. For example, the equation c² = a + b suggests a linear relationship rather than a geometric one, and both c = a + b² and a + b = c do not adhere to the principles outlined by the Pythagorean Theorem. Hence, a² + b² = c² accurately captures the essence of this important mathematical principle.