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