Question

identify a segment skew to $overline{ab}$ using the figure shown. assume lines and planes that appear to be parallel or perpendicular are parallel or perpendicular, respectively.
a) $overline{dc}$
b) $overline{eh}$
c) $overline{hg}$
d) $overline{ef}$

Explanation:

Step1: Recall skew - line definition

Skew lines are non - parallel and non - intersecting lines in 3 - D space.

Step2: Analyze each option

• $\overline{DC}$ is parallel to $\overline{AB}$, so it is not skew.
• $\overline{EH}$ is parallel to $\overline{DC}$ and also parallel to $\overline{AB}$ in the 3 - D structure, so it is not skew.
• $\overline{HG}$ is not in the same plane as $\overline{AB}$, is not parallel to $\overline{AB}$, and does not intersect $\overline{AB}$, so it is skew.
• $\overline{EF}$ is parallel to $\overline{AB}$, so it is not skew.

Answer:

C. $\overline{HG}$