In a right triangle, what does the Pythagorean theorem state?

The Pythagorean theorem is a fundamental principle in geometry that specifically relates to right triangles. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle, denoted as c) is equal to the sum of the squares of the lengths of the other two sides (denoted as a and b). This relationship is expressed mathematically as a² + b² = c².

This theorem is crucial for solving problems involving right triangles, as it allows you to calculate the length of one side if the lengths of the other two sides are known. It also forms the basis for various applications, including distance calculations in coordinate geometry and trigonometry. Understanding this theorem is essential for mastering properties of triangles and applying them in both theoretical and practical contexts.

The first option incorrectly states a linear relationship rather than a squared relationship. The third option refers to the angles of a triangle, which is unrelated to the Pythagorean theorem and instead pertains to the concept that the angle measures of a triangle sum up to 180 degrees. The last option incorrectly portrays a different mathematical relationship involving subtraction instead of addition.