Equivalence Relations

Example #1: Triangles whose angles match up (even if their corresponding sides aren't equal) are called similar triangles. The relation that matches similar triangles to one another (let's call it $\text{Sim-Triangle}$) is an equivalence relation.

Example #2: Triangles whose angles match up and whose corresponding sides are equal are called congruent triangles and create a relation (let's call it $\text{Cong-Triangle}$) that is an equivalence relation, too.