Equivalence Classes Math Example 2

Solution

1. 1
   Reflexive: Every triangle is congruent to itself (by the identity transformation). True.
2. 2
   Symmetric: If $T_1 \cong T_2$, then $T_2 \cong T_1$ (congruence is symmetric). True.
3. 3
   Transitive: If $T_1 \cong T_2$ and $T_2 \cong T_3$, then $T_1 \cong T_3$ (compose the rigid motions). True.
4. 4
   Conclusion: congruence is an equivalence relation. Each equivalence class consists of all triangles with the same shape and size.