1. The problem is to understand why the line segments $ST$ and $SN$ are congruent. 2. To determine if two segments are congruent, we check if they have the same length. 3. The formula for the length of a segment between points $S(x_1,y_1)$ and $T(x_2,y_2)$ is $$\text{Length} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 4. Similarly, the length of segment $SN$ is $$\sqrt{(x_N - x_S)^2 + (y_N - y_S)^2}$$ 5. If the problem states or shows that these lengths are equal, then $ST \cong SN$ by definition of congruent segments. 6. Sometimes, congruence is shown by properties such as midpoint, bisector, or symmetry which imply equal lengths. 7. Without coordinates, congruence can be justified by geometric properties or given equal measures. 8. Therefore, $ST$ is congruent to $SN$ because they have equal lengths either by calculation or geometric reasoning.