Horizontal plane A and vertical plane B intersect at a line. Line n is vertical on plane B and forms a right angle with horizontal line m on plane A. Line l is diagonal on plane A.
Are the lines in the diagram perpendicular, parallel, skew, or none of these?

l and m: 

l and n: 

m and n: 


To understand the relationship between the lines in the diagram, we need to analyze their orientations and the planes they lie on.

- **Plane A** is horizontal, and **Plane B** is vertical.
- **Line n** is vertical and lies on **Plane B**.
- **Line m** is horizontal and lies on **Plane A**.
- **Line l** is diagonal on **Plane A**.

Let's examine the relationships between the lines:

1. **l and m**:  
   Both **l** and **m** lie on **Plane A**. Since **l** is diagonal and **m** is horizontal, they are not parallel. However, without additional information on their angles, we cannot say they are perpendicular. Therefore, **l and m** are neither parallel nor perpendicular.

2. **l and n**:  
   **Line l** lies on the horizontal **Plane A**, while **Line n** is vertical on **Plane B**. Since **l** lies on the horizontal plane and **n** is vertical, these two lines are neither parallel nor perpendicular. Moreover, they lie on different planes, meaning they do not intersect. Hence, **l and n** are **skew** lines.

3. **m and n**:  
   **Line m** is horizontal on **Plane A**, and **Line n** is vertical on **Plane B**. Since **n** is vertical and **m** is horizontal, they meet at a right angle, so **m and n** are **perpendicular**.

### Summary:
- **l and m**: Neither parallel nor perpendicular.
- **l and n**: Skew.
- **m and n**: Perpendicular.

Would you like further details or have any other questions?

Here are 5 related questions to explore further:
1. What conditions are necessary for two lines to be considered skew?
2. Can two lines on the same plane ever be skew?
3. How do we determine if two diagonal lines on the same plane are perpendicular?
4. What is the relationship between two lines that intersect at an angle other than 90 degrees?
5. How does the orientation of planes affect the relationships between the lines?

**Tip**: To determine if two lines are skew, check if they lie on different planes and do not intersect.

Horizontal plane A and vertical plane B intersect at a line. Line n is vertical on plane B and forms a right angle with horizontal line m on plane A. Line l is diagonal on plane A.
Are the lines in the diagram perpendicular, parallel, skew, or none of these?

l and m:

l and n:

m and n:

Explore the relationships between lines on intersecting horizontal and vertical planes. Learn about perpendicular, parallel, and skew lines with a detailed solution, analyzing lines n, m, and l on planes A and B. This problem is suitable for students in Grades 9-12.

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