What does 'A² + B² = C²' represent in geometry?

The equation 'A² + B² = C²' represents the Pythagorean theorem, which is a fundamental principle in geometry. This theorem specifically applies to right-angled triangles. According to the Pythagorean theorem, the sum of the squares of the lengths of the two shorter sides (often denoted as A and B) is equal to the square of the length of the hypotenuse (denoted as C), which is the side opposite the right angle. This relationship helps in determining the lengths of the sides of a right triangle when the lengths of two sides are known.

In practical applications, this theorem is instrumental for various fields, including architecture, engineering, and various calculations involving distance and angles. Recognizing the equation as a representation of the Pythagorean theorem is crucial for solving problems involving right triangles in both academic settings and real-world situations.