What defines the hypotenuse in a right triangle?

The hypotenuse in a right triangle is defined as the side opposite the right angle, and it is always the longest side of the triangle. This is fundamental to the properties of right triangles as established by the Pythagorean theorem, which states that in a right triangle with legs of lengths (a) and (b) and hypotenuse of length (c), the relationship (a^2 + b^2 = c^2) holds true.

Since the hypotenuse is opposite the right angle, which is the largest angle in the triangle, it inherently becomes the longest side compared to the two other sides, known as the legs, which form the right angle. Therefore, recognizing that the hypotenuse is always the longest side is critical to analyzing and understanding right triangles.