What characterizes a right triangle?

A right triangle is specifically characterized by having one angle that measures exactly 90 degrees. This unique property distinguishes it from other types of triangles. In a right triangle, the side opposite the right angle is called the hypotenuse, which is the longest side of the triangle. The presence of this right angle is critical because it establishes the foundation for various mathematical concepts, including the Pythagorean theorem, which relates the lengths of the sides in right triangles.

The other options do not apply to the definition of a right triangle. For instance, while it is true that an acute triangle has all angles less than 90 degrees, a right triangle has exactly one angle that is 90 degrees. The option about two sides being of equal length refers to an isosceles triangle, which can have various angle measures, including right angles but does not define a right triangle. Lastly, the option regarding all sides being different lengths describes a scalene triangle, which does not pertain to the definition of a right triangle either. Thus, the correct choice emphasizes the defining characteristic of a right triangle being its 90-degree angle.