Question

1. what kind of relationship do $overleftrightarrow{cf}$ and $overline{gh}$ have?

parallel
congruent
skew
perpendicular

Explanation:

Step1: Analyze parallel lines

Parallel lines are coplanar and never intersect. $\overleftrightarrow{CF}$ is a vertical line, and $\overline{GH}$ is a horizontal line on the bottom - face of the cube. They are not parallel.

Step2: Analyze congruent segments

Congruent segments have the same length. There is no information given about their lengths being equal, and from the nature of the cube's edges (different - direction edges), we can't assume congruence based on the relationship type (we need specific length - equality info for congruence as a geometric property here, not just visual in a general cube).

Step3: Analyze skew lines

Skew lines are non - coplanar, non - intersecting. $\overleftrightarrow{CF}$ is not on the same plane as $\overline{GH}$ (one is vertical, one is on the bottom - face horizontal) and they do not intersect.

Step4: Analyze perpendicular lines

Perpendicular lines intersect at a right - angle. $\overleftrightarrow{CF}$ and $\overline{GH}$ do not intersect.

Answer:

Skew