Question

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

Explanation:

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

Open the compass to the length of \(\overline{WX}\) by placing the needle at \(W\) and the pencil at \(X\).

Step2: Draw a ray from \(P\)

Use the straightedge to draw a ray with endpoint \(P\).

Step3: Mark the congruent segment

Place the needle of the compass at \(P\) and draw an arc intersecting the ray. Label the intersection point \(Q\). Then \(\overline{PQ}\) is congruent to \(\overline{WX}\).

Answer:

To construct a segment congruent to \(\overline{WX}\) with endpoint \(P\):

1. Measure \(\boldsymbol{\overline{WX}}\): Open the compass so the needle is at \(W\) and the pencil is at \(X\) (this sets the compass to the length of \(\overline{WX}\)).
2. Draw a ray from \(\boldsymbol{P}\): Use the straightedge to draw a ray starting at \(P\) (extending in any direction, e.g., horizontally or vertically).
3. Mark the congruent segment: Place the compass needle at \(P\) and draw an arc that intersects the ray. Label the intersection point (e.g., \(Q\)). The segment \(\overline{PQ}\) is congruent to \(\overline{WX}\).

(Note: In a digital construction tool, use the compass to measure \(\overline{WX}\), then use the compass to mark the same length from \(P\) on a ray drawn from \(P\) with the straightedge.)