Question

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

Explanation:

Step1: Open the compass to measure the length of \(\overline{AB}\)

Use the compass to measure the distance between points \(A\) and \(B\).

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

With the compass still set to the length of \(\overline{AB}\), place the compass point at \(P\) and draw an arc.

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

Using the straightedge, draw a segment from \(P\) to a point \(Q\) on the arc. The segment \(\overline{PQ}\) is congruent to \(\overline{AB}\).

Answer:

Constructed segment \(\overline{PQ}\) is congruent to \(\overline{AB}\) with endpoint \(P\).