Answer
$\overline{MP}$ is the pair of parts that are congruent by Identity.
Work Step by Step
The pair of parts that are congruent by Identity is the side or the angle that both triangles have as its own side or angle.
In this image, we can see that both triangles have $\overline{MP}$ as a side of its own.
Therefore, here $\overline{MP}$ is the pair of parts that are congruent by Identity.