Question

which segment is skew to \\(\overline{eb}\\)?

use for #1-4

\\(\bigcirc\\) \\(\overline{df}\\)
\\(\bigcirc\\) \\(\overline{de}\\)
\\(\bigcirc\\) \\(\overline{fc}\\)
\\(\bigcirc\\) \\(\overline{bc}\\)

Explanation:

🆕 New Concept Discovered: Skew Lines in 3D Space
Lines that never cross and are not parallel.

Step 1: Understand skew lines

In three-dimensional geometry, two line segments are skew if they satisfy two conditions:

1. They do not intersect (they never touch).
2. They are not parallel (they go in different directions).

This means they must lie in completely different, non-parallel planes.

Step 2: Analyze the target segment

We are looking for a segment skew to \(\overline{EB}\).

Let's locate \(\overline{EB}\) on the triangular prism:

• It is a vertical dashed segment connecting the back-bottom vertex \(E\) to the top vertex \(B\).

Step 3: Evaluate the given options

• \(\overline{DF}\): This is a horizontal segment along the bottom front. It lies in a completely different plane from \(\overline{EB}\), does not intersect \(\overline{EB}\), and is not parallel to it. Therefore, \(\overline{DF}\) is skew to \(\overline{EB}\).
• \(\overline{DE}\): This segment shares the vertex \(E\) with \(\overline{EB}\), meaning they intersect. Thus, they cannot be skew.
• \(\overline{FC}\): This is a vertical segment on the right side. Since \(\overline{EB}\) is also a vertical segment, \(\overline{FC}\) is parallel to \(\overline{EB}\). Thus, they cannot be skew.
• \(\overline{BC}\): This segment shares the vertex \(B\) with \(\overline{EB}\), meaning they intersect. Thus, they cannot be skew.

Answer:

\(\overline{DF}\)