Prove that ML = PL using the given figure and congruence criteria.

From the figure, we can observe:

• $\angle M = \angle P$ (indicated by the arc marks).
• $\angle LOM = 90^\circ$ and $\angle LOP = 90^\circ$ (indicated by the right angle symbol at $O$, meaning $LO \perp MP$).
• $LO$ is a common side to both $\triangle LOM$ and $\triangle LOP$.

Consider $\triangle LOM$ and $\triangle LOP$:

1. $\angle M = \angle P$ (Given)
2. $\angle LOM = \angle LOP = 90^\circ$ (Given, as $LO$ is perpendicular to $MP$)
3. $LO = LO$ (Common side)

By the Angle-Angle-Side (AAS) congruence criterion, $\triangle LOM \cong \triangle LOP$.

Since $\triangle LOM \cong \triangle LOP$, their corresponding parts are equal.
Therefore, the side $\overline{ML}$ in $\triangle LOM$ corresponds to the side $\overline{PL}$ in $\triangle LOP$.
Thus, $\overline{ML} = \overline{PL}$.

This completes the proof.

$\boxed{\text{Proven that } \overline{ML} = \overline{PL}}$