To determine which angle in triangle △DEF has the largest measure, you can use an important role in geometry: the largest angle in a triangle is always opposite the longest side. This rule stems from the properties of triangles, where longer sides are associated with larger opposite angles.
For example, if side DE is the longest side in △DEF, then angle ∠F, which is opposite DE, will have the largest measure. This principle is a direct consequence of the triangle inequality theorem and helps in understanding the relationship between a triangle’s angles and sides. By identifying the longest side, you can quickly determine the largest angle.