Question

use the compass and straightedge to construct a segment congruent to $overline{mn}$ with endpoint $p$.

Explanation:

Step1: Set compass width

Place the compass' needle on point $M$ and the pencil - lead on point $N$. This sets the width of the compass to the length of segment $\overline{MN}$.

Step2: Draw an arc

Without changing the width of the compass, place the compass' needle on point $P$. Then draw an arc.

Step3: Mark the new point

Use the straightedge to draw a ray starting from point $P$ that intersects the arc. Mark the intersection point as $Q$. The segment $\overline{PQ}$ is congruent to $\overline{MN}$.

Answer:

The constructed segment $\overline{PQ}$ is congruent to $\overline{MN}$.