Question

use the compass and straightedge to construct a segment congruent to \\(\overline{rs}\\) with endpoint \\(p\\).

Explanation:

Step1: Set compass width

Open compass to length of \( \overline{RS} \) (place one end at \( R \), the other at \( S \)).

Step2: Draw arc from \( P \)

With compass set, place the needle at \( P \) and draw an arc (this arc will have a radius equal to \( RS \)).

Step3: Mark endpoint \( Q \)

Choose a point \( Q \) on the arc (this makes \( \overline{PQ} \) congruent to \( \overline{RS} \)).

Step4: Draw segment \( \overline{PQ} \)

Use straightedge to connect \( P \) and \( Q \), forming \( \overline{PQ} \cong \overline{RS} \).

Answer:

Constructed segment \( \overline{PQ} \) (where \( Q \) is on the arc from \( P \) with radius \( RS \)) congruent to \( \overline{RS} \).