Question

1. given the diagram below, which pair of lines are skew? a. \\(\overline{de}\\) and \\(\overline{cf}\\) b. \\(\overline{ef}\\) and \\(\overline{bc}\\) c. \\(\overline{ea}\\) and \\(\overline{ad}\\) d. \\(\overline{dc}\\) and \\(\overline{ab}\\)

Explanation:

Step1: Recall skew lines definition

Skew lines are non - parallel, non - intersecting, and lie in different planes.

Step2: Analyze Option A

$\overline{DE}$ and $\overline{CF}$: These lines are parallel (since the figure is a prism - like shape, and these lines are on the lateral faces which are parallel). So they are not skew.

Step3: Analyze Option B

$\overline{EF}$ and $\overline{BC}$: $\overline{EF}$ and $\overline{BC}$ are in different planes, they are not parallel, and they do not intersect. So they satisfy the definition of skew lines.

Step4: Analyze Option C

$\overline{EA}$ and $\overline{AD}$: These two lines intersect at point $A$, so they are not skew.

Step5: Analyze Option D

$\overline{DC}$ and $\overline{AB}$: These lines are parallel (since in the prism - like shape, these are opposite sides of the base and top faces which are parallel), so they are not skew.

Answer:

B. $\overline{EF}$ and $\overline{BC}$