Use the compass and straightedge to construct a segment congruent to $$ \overline{W X} $$ with endpoint $$ P $$. Constructing congruent line segments

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1. Locate the given segment $$ \overline{WX} $$ and the point $$ P $$ (which is not necessarily collinear with $$ WX $$).

2. Open the compass to the length of $$ \overline{WX} $$ (i.e., adjust the compass so that the distance between its points equals the length of $$ WX $$).

3. With the compass set to this width, place the compass point on $$ P $$ and draw an arc. This arc represents all points that are exactly the distance $$ WX $$ from $$ P $$.

4. Mark the point $$ Q $$ where the arc intersects a ray emanating from $$ P $$ (you may construct any ray from $$ P $$ as long as the arc intersects it).

5. Draw the segment $$ \overline{PQ} $$ with the straightedge.

Since the compass width was set equal to $$ WX $$, by the definition of a circle, $$ \overline{PQ} $$ is congruent to $$ \overline{WX} $$. Thus, the desired construction is complete:

$$
\overline{PQ} \cong \overline{WX}
$$
To construct a segment congruent to $$ \overline{WX} $$ with endpoint $$ P $$, follow these steps: 1. **Set Compass Width**: Adjust the compass to the length of $$ \overline{WX} $$. 2. **Draw Arc**: Place the compass point on $$ P $$ and draw an arc to mark the desired length. 3. **Mark Point $$ Q $$**: Identify the intersection point $$ Q $$ of the arc with a ray from $$ P $$. 4. **Draw Segment $$ \overline{PQ} $$**: Use the straightedge to connect $$ P $$ and $$ Q $$. Since the compass was set to the length of $$ \overline{WX} $$, $$ \overline{PQ} $$ is congruent to $$ \overline{WX} $$.

Use the compass and straightedge to construct a segment congruent to \( \overline{W X} \) with endpoint \( P \). Constructing congruent line segments

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