What is the primary characteristic of a right triangle?

A right triangle is primarily characterized by having one right angle, which is defined as an angle measuring exactly 90 degrees. This specific property distinguishes right triangles from other types of triangles, such as acute triangles (where all angles are less than 90 degrees) and obtuse triangles (where one angle is greater than 90 degrees). The presence of a right angle enables the application of various mathematical principles and theorems, most notably the Pythagorean theorem, which relates the lengths of the sides of the triangle.

While other characteristics about triangles can mention side lengths or angles, they do not define the essential nature of a right triangle as clearly as the existence of a right angle does. For instance, an equilateral triangle features all angles equal and all sides equal, but this does not apply to right triangles.