https://file.aiquickdraw.com/mathbot/file/17297915382000lthf2fk.jpg

The image contains four geometric statements in Russian, and you're asked to choose all correct ones. Here’s a translation of each statement:

1. **If a line \( l_1 \) lying in plane \( \pi_1 \) is parallel to line \( l_2 \) lying in plane \( \pi_2 \), then \( \pi_1 \parallel \pi_2 \).**

2. **Two skew lines do not belong to the same plane.**

3. **Let two skew lines be given, then there exists a plane in which they are parallel, and there is only one such plane.**

4. **Through two intersecting lines, it is always possible to draw a plane, and only one plane.**

### Analysis:

1. **Statement 1**: False. Even if lines \( l_1 \) and \( l_2 \) are parallel, it does not necessarily mean that the planes \( \pi_1 \) and \( \pi_2 \) are parallel. They could intersect while still having the lines parallel in different planes.

2. **Statement 2**: True. Skew lines are defined as non-parallel lines that do not intersect and do not lie in the same plane.

3. **Statement 3**: False. Skew lines, by definition, cannot be parallel within a plane, because they do not lie in the same plane at all.

4. **Statement 4**: True. Two intersecting lines determine a unique plane, meaning only one plane can contain both lines.

### Correct answers:
- Statement 2 (Two skew lines do not belong to the same plane).
- Statement 4 (Through two intersecting lines, it is always possible to draw a plane, and only one plane).

Would you like further details on these concepts?

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Here are five related questions:
1. What is the difference between skew lines and parallel lines?
2. Can two parallel planes intersect at some point?
3. How do you determine the equation of a plane containing two intersecting lines?
4. What conditions must be met for two lines to lie in the same plane?
5. Can more than one plane pass through two non-parallel lines?

**Tip:** Always visualize skew lines as non-intersecting and non-parallel lines that exist in different planes.

Укажите все верные утверждения о прямых и плоскостях.

Learn how to determine correct geometric statements involving skew lines, intersecting lines, and planes. This problem includes concepts about lines not belonging to the same plane, and drawing unique planes through intersecting lines. Suitable for Grades 9-11.

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