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 on point $M$ and extend the other leg to point $N$. This sets the compass width equal to the length of segment $\overline{MN}$.

Step2: Draw an arc

With the compass width set as above, place the compass on point $P$ and draw an arc.

Step3: Mark the endpoint

Choose a point $Q$ on the arc. The segment $\overline{PQ}$ is congruent to $\overline{MN}$.

Answer:

A segment $\overline{PQ}$ has been constructed such that $\overline{PQ}\cong\overline{MN}$ where $P$ is the given endpoint.