Question

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

Explanation:

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

Open the compass so that its two ends align with points \( A \) and \( B \). This sets the compass width equal to the length of \( \overline{AB} \).

Step2: Draw an arc with center \( P \)

Place the compass point at \( P \). Then, draw an arc (using the width set in Step1) on the paper.

Step3: Mark a point \( Q \) on the arc

Use the straight - edge to draw a line from \( P \) to any point \( Q \) on the arc. The segment \( \overline{PQ} \) is congruent to \( \overline{AB} \).

Answer:

Construct \( \overline{PQ} \) as described above.