Question

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

Explanation:

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

Use compass: Place compass point on \( C \), adjust to \( D \) to set radius \( CD \).

Step2: Draw congruent segment from \( P \)

Place compass point on \( P \), draw an arc (using the radius from Step1) on a line (using straightedge) through \( P \). Mark intersection as \( Q \). So \( \overline{PQ} \cong \overline{CD} \).

Answer:

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