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Which line is skew to line 2 in the diagram?

line 1
line 4
line 5
line 3

In the diagram, line \( \ell_2 \) is positioned on the side of the rectangular prism, and we need to determine which line is **skew** to it. Skew lines are lines that do not intersect and are not parallel.

- **Line \( \ell_1 \)**: It appears on a different face of the rectangular prism and does not intersect with \( \ell_2 \). It is also not parallel, making it skew to \( \ell_2 \).
- **Line \( \ell_3 \)**: It lies on the same plane as \( \ell_2 \) (side of the prism) and is parallel to \( \ell_2 \), so it cannot be skew.
- **Line \( \ell_4 \)**: This line is perpendicular to the plane of \( \ell_2 \) and would intersect it if extended, meaning it is not skew.
- **Line \( \ell_5 \)**: This line is also parallel to \( \ell_2 \) (on the same side), so it is not skew.

Thus, **line \( \ell_1 \)** is the line skew to \( \ell_2 \).

Would you like further details or clarification?

Here are 5 related questions for further understanding:
1. What are the defining properties of skew lines?
2. How do parallel and perpendicular lines differ from skew lines in 3D geometry?
3. Can two lines be skew if they are in the same plane?
4. How do you determine if two lines are parallel or skew in 3D space?
5. What is the relationship between skew lines and angles in 3D geometry?

**Tip:** In three-dimensional geometry, two lines that are neither parallel nor intersecting are always skew lines.

Which line is skew to line 2 in the diagram?

Learn how to determine which line is skew to line 2 in the diagram of a rectangular prism. This geometry problem involves 3D geometry concepts, specifically skew lines, parallelism, and perpendicularity. Suitable for students in Grades 9-12.

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