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.
options:
a) \\( \overline{dc} \\)

b) \\( \overline{eh} \\)

c) \\( \overline{hg} \\)

d) \\( \overline{ef} \\)

(figure of a prism with vertices labeled a, b, c, d, e, f, g, h)

Explanation:

Step1: Recall Skew Lines Definition

Skew lines are non - parallel, non - intersecting, and lie in different planes. First, analyze the relationship of each option with \(\overline{AB}\).

Step2: Analyze Option A (\(\overline{DC}\))

\(\overline{DC}\) and \(\overline{AB}\) are parallel (since in the rectangular prism - like figure, \(AB\) and \(DC\) are opposite sides of a face, so they are parallel). So \(\overline{DC}\) is not skew to \(\overline{AB}\).

Step3: Analyze Option B (\(\overline{EH}\))

\(\overline{EH}\) and \(\overline{AB}\): \(\overline{AB}\) is in the front - bottom face (or related face), \(\overline{EH}\) is in the top - back face. They are non - parallel and non - intersecting, lying in different planes.

Step4: Analyze Option C (\(\overline{HG}\))

\(\overline{HG}\) and \(\overline{AB}\): \(\overline{HG}\) is parallel to \(\overline{DC}\) (and thus parallel to \(\overline{AB}\)) as they are opposite sides of a face in the prism - like structure. So \(\overline{HG}\) is parallel to \(\overline{AB}\), not skew.

Step5: Analyze Option D (\(\overline{EF}\))

\(\overline{EF}\) and \(\overline{AB}\): \(\overline{EF}\) is parallel to \(\overline{DC}\) (and thus parallel to \(\overline{AB}\)) as they are opposite sides of a face in the prism - like structure. So \(\overline{EF}\) is parallel to \(\overline{AB}\), not skew.

Answer:

B. \(\overline{EH}\)