In a 45-45-90 triangle, what is the relationship between the legs?

In a 45-45-90 triangle, which is an isosceles right triangle, the two legs are always equal in length. This specific type of triangle is formed when both angles opposite the legs measure 45 degrees. Because of the properties of right triangles, particularly those with equal acute angles, the lengths of the legs must be the same to maintain the angle measurements.

Furthermore, the relationship between the lengths of the legs and the hypotenuse in a 45-45-90 triangle can be described with the formula: if each leg has a length of ( x ), the hypotenuse will be ( x\sqrt{2} ). This reinforces the idea that while the hypotenuse is longer than each leg, the legs themselves maintain equal lengths.

The other relationships indicated in the options do not hold true due to the defining characteristics of a 45-45-90 triangle. Therefore, recognizing that both legs are of equal length is key to understanding this special triangle.