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What is the intersection of plane *K* and line *c*? 
 

To find the intersection of plane \( K \) (which we'll assume to be the plane containing points \( K \), \( P \), \( S \), and \( T \)) and line \( c \), we need to identify the point where this line \( c \) meets the plane \( K \).

From the diagram:
- **Line \( c \)** appears to pass through points \( R \) and \( Q \), which lie on the lower plane containing points like \( L \), \( M \), \( N \), \( O \), and \( U \).
- Since line \( c \) is below the plane \( K \), the intersection point would be where line \( c \) extends upwards to meet plane \( K \).

Looking at the diagram, it seems that line \( c \) and plane \( K \) do not actually intersect directly. The projection of line \( c \) intersects with the lower plane, and there is no indication of line \( c \) extending upwards to the upper plane \( K \).

Therefore, based on the diagram:
- **There is no intersection** between line \( c \) and plane \( K \) because line \( c \) lies completely on the lower plane and does not extend to the upper plane \( K \).

If you have any further questions or need additional details, feel free to ask!

Here are some follow-up questions to consider:
1. What would happen if line \( c \) were extended to intersect the plane \( K \)?
2. How would you determine if a line and a plane are parallel?
3. Can a line intersect two different planes at the same time?
4. What are the conditions for a line to be perpendicular to a plane?
5. How would the diagram change if the planes were not parallel?

**Tip:** When analyzing the intersection of a line and a plane, it's helpful to extend the line in both directions to see if it will eventually intersect the plane.

Explore the intersection of plane K and line c in geometry. Learn how to determine if and where a line intersects a plane and analyze specific scenarios. Suitable for high school students studying geometry.

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