Question

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

Explanation:

Step1: Measure length of \( \overline{FG} \)

Use compass: Place compass point on \( F \), adjust to \( G \) to set radius \( FG \).

Step2: Draw congruent segment from \( P \)

Place compass point on \( P \), draw an arc (with radius \( FG \)) on a line (using straightedge to draw line from \( P \) first if needed). Mark intersection as \( Q \), so \( \overline{PQ} \cong \overline{FG} \).

Answer:

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