Question

which two line segments are skew?
$overline {ei}$ and $overline {gk}$
$overline {de}$ and $overline {ge}$
$overline {hi}$ and $overline {df}$
$overline {gk}$ and $overline {dh}$

Explanation:

Step1: Recall the definition of skew lines

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

Step2: Analyze each option

• For \(\overline{EI}\) and \(\overline{GK}\):
• Assume a 3 - D figure (since skew lines are in 3 - D).
• \(\overline{EI}\) and \(\overline{GK}\) are non - parallel and non - intersecting.
• For \(\overline{DE}\) and \(\overline{GE}\): They intersect at point \(E\), so they are not skew.
• For \(\overline{HI}\) and \(\overline{DF}\): They are parallel (assuming a regular 3 - D structure like a rectangular prism), so they are not skew.
• For \(\overline{GK}\) and \(\overline{DH}\): They are parallel (assuming a regular 3 - D structure like a rectangular prism), so they are not skew.

Answer:

\(\overline{EI}\) and \(\overline{GK}\)