1. The problem asks to construct a line segment congruent to the segment $\overline{GH}$.\n\n2. To solve this, we need to understand that two line segments are congruent if they have the same length.\n\n3. The length of $\overline{GH}$ is the distance between points $G$ and $H$. Since $\overline{GH}$ is vertical, its length is the difference in the $y$-coordinates of $G$ and $H$.\n\n4. Suppose the length of $\overline{GH}$ is $L$. We want to construct a segment $\overline{DC}$ on the right side such that $|\overline{DC}| = L$.\n\n5. Using a compass, place the compass point on $G$ and adjust it to reach $H$. This sets the compass width to $L$.\n\n6. Without changing the compass width, place the compass point on $D$ and draw an arc intersecting the vertical line through $D$. Label the intersection point as $C$.\n\n7. The segment $\overline{DC}$ is now congruent to $\overline{GH}$ because it has the same length $L$.\n\nFinal answer: $\overline{DC} \cong \overline{GH}$