Question

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

Explanation:

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

Use the compass to measure the length of \(\overline{AB}\). Place the compass's needle at point \(A\) and adjust the compass so that the pencil end is at point \(B\).

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

Without changing the compass's width (which is set to the length of \(\overline{AB}\)), place the compass's needle at point \(P\) and draw an arc.

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

Use the straightedge to draw a ray starting from \(P\) in any direction. Mark a point \(Q\) where the ray intersects the arc. Then \(\overline{PQ}\) is congruent to \(\overline{AB}\).

Answer:

Construct \(\overline{PQ}\) as described above so that \(\overline{PQ}\cong\overline{AB}\)