he largest angle of a triangle is opposite the side, and the smallest angle is opposite the side.

In a triangle, the relationships between the angles and the sides are fundamental principles of geometry. According to the triangle inequality theorem, the largest angle is always opposite the longest side, while the smallest angle is opposite the shortest side. This means that if you know the lengths of the sides of a triangle, you can determine the relative sizes of the angles.

Explanation:

1. Longest Side and Largest Angle: If side $c$ is the longest side in triangle $ABC$, then angle $C$ will be the largest angle. Mathematically, if $a < b < c$, then $\angle A < \angle B < \angle C$.

2. Shortest Side and Smallest Angle: Conversely, if side $a$ is the shortest side, then angle $A$ will be the smallest angle. Thus, the relationship can be summarized as:

   • Longest side $\Rightarrow$ Largest angle
   • Shortest side $\Rightarrow$ Smallest angle

This principle helps in solving various geometrical problems, including those involving angles, areas, and side lengths of triangles. In practical applications, this rule can assist in calculating unknown angles and enhancing our understanding of triangle properties in both theoretical mathematics and real-world scenarios.