Question

8 of the four options, which line segment is skew to \\( \overline { g f } \\)?
a \\( \overline { a g } \\)
b \\( \overline { g h } \\)
c \\( \overline { b d } \\)
d \\( \overline { d e } \\)

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

• Option A: \(\overline{AG}\)

\(\overline{AG}\) and \(\overline{GF}\) intersect at point \(G\), so they are not skew.

• Option B: \(\overline{GH}\)

\(\overline{GH}\) and \(\overline{GF}\) intersect at point \(G\), so they are not skew.

• Option C: \(\overline{BD}\)

\(\overline{BD}\) and \(\overline{GF}\) are non - parallel and non - intersecting.

• Option D: \(\overline{DE}\)

\(\overline{DE}\parallel\overline{GF}\) (since in a rectangular prism, opposite sides of a parallelogram - like face are parallel), so they are not skew.

Answer:

C. \(\overline{BD}\)