Answer
We can use the SAS theorem to prove that $\triangle LKM$ is congruent to $\triangle NMK$. Corresponding lines of congruent triangles are congruent, so $\overline{KN} ≅ \overline{ML}$.
Work Step by Step
1. $\overline{KL}$ is marked congruent to $\overline{MN}$.
2. $\overline{KM}$ is shared by both triangles, so it is also congruent.
3. $\overline{KL}$ is parallel to $\overline{MN}$; therefore, $\overline{KM}$ acts like a transversal, so $\angle LKM$ and $\angle NMK$ are congruent because they are alternate interior angles.
Now, we have two sides and an included angle that are congruent; therefore, we can use the SAS theorem to prove that $\triangle LKM$ is congruent to $\triangle NMK$. Corresponding lines of congruent triangles are congruent, so $\overline{KN} ≅ \overline{ML}$.
