Question

in the triangular prism shown below, which lines are skew?
dg and gh
hi and fi
gi and ef
df and fi

Explanation:

Step1: Recall the definition of skew lines

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

Step2: Analyze each pair

• For \(\overleftrightarrow{DG}\) and \(\overleftrightarrow{GH}\): They intersect at point \(G\), so they are not skew.
• For \(\overleftrightarrow{HI}\) and \(\overleftrightarrow{FI}\): They intersect at point \(I\), so they are not skew.
• For \(\overleftrightarrow{GI}\) and \(\overleftrightarrow{EF}\): They are non - parallel and non - intersecting.
• For \(\overleftrightarrow{DF}\) and \(\overleftrightarrow{FI}\): They intersect at point \(F\), so they are not skew.

Answer:

\(\overleftrightarrow{GI}\) and \(\overleftrightarrow{EF}\)