Geometry Regents Practice Exam

A triangle with all sides of different lengths is defined as a scalene triangle. This means that none of its sides are equal, which also implies that all three angles within the triangle are different. The distinguishing feature of scalene triangles is the uniqueness of side lengths and angle measures, leading to a variety of shapes and configurations.

In contrast, an equilateral triangle has all three sides equal, and consequently, all angles are also equal. An isosceles triangle has at least two sides of equal length, which means it cannot have all sides different. A right triangle is defined by having one angle equal to 90 degrees, but it can be scalene if all sides are of different lengths; however, this definition does not specifically address the uniqueness of side lengths on its own. Thus, within the context of the question, scalene specifically highlights the characteristic of having all different side lengths.