How is a right triangle defined in terms of its angles?

A right triangle is defined specifically by the presence of one angle that measures exactly 90 degrees. This characteristic is what differentiates a right triangle from other types of triangles. In a right triangle, the right angle indicates that the triangle adheres to the Pythagorean theorem, which establishes a relationship between the lengths of the sides of the triangle. The presence of this right angle also allows for the classification of the other two angles as acute angles, as the sum of angles in any triangle must equal 180 degrees. Thus, with one angle fixed at 90 degrees, the other two angles must each be less than 90 degrees, confirming that they are acute.

In contrast, triangles characterized by angles all being less than 90 degrees, no right angles, or exclusively having acute angles do not meet the criteria for classification as a right triangle. Therefore, the definition focusing on the presence of one right angle is crucial for identifying a triangle as a right triangle.