In a right triangle, what is the relationship between the lengths of the sides known as?

In a right triangle, the relationship between the lengths of the sides is defined by the Pythagorean theorem. This theorem states that for 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 can be expressed mathematically as ( c^2 = a^2 + b^2 ), where ( c ) is the length of the hypotenuse, and ( a ) and ( b ) are the lengths of the other two sides.

This foundational principle is critical in various applications, including geometry, trigonometry, and various fields of engineering and physics, as it allows one to solve for unknown side lengths given certain information. Understanding this relationship enables students to engage with more complex mathematical concepts and problems involving right triangles.

The other relationships mentioned, such as trigonometric ratios, angle properties, and circle theorems, pertain to different aspects of triangles or circles but do not specifically define the relationship between the side lengths in a right triangle.