In a 45-45-90 triangle, the hypotenuse is labeled as "D. None of the above." In a 45-45-90 triangle, the hypotenuse is not labeled as "opposite," "adjacent," or "both legs." The hypotenuse is a distinct side of the triangle and does not have a specific label among the given options.
In a 45-45-90 triangle, all three sides have specific labels. The two congruent legs, which are the sides opposite the 45-degree angles, are labeled as "A" and "B." The hypotenuse, which is the side opposite the right angle, does not have a specific label assigned to it among the options A, B, or C.
To understand why the hypotenuse is not labeled as "opposite," "adjacent," or "both legs," it's important to know the definitions of these terms.
- "Opposite" and "adjacent" are terms commonly used in the context of right triangles in trigonometry. They refer to the sides relative to a specific angle, not specifically the hypotenuse. In a 45-45-90 triangle, there is no specific angle labeled as "opposite" or "adjacent" since the two legs are congruent.
- "Both legs" is also an incorrect label for the hypotenuse since it is a distinct side of the triangle, separate from the congruent legs.
Therefore, the correct answer is D. None of the above, as the hypotenuse in a 45-45-90 triangle does not fall into the given options of "opposite," "adjacent," or "both legs."