In Euclidean geometry, meridians are not parallel.

Here’s why:

• Meridians are imaginary lines that run from the North Pole to the South Pole, passing through the poles and connecting various points on Earth's surface. They are a type of longitude line.
• In Euclidean geometry, parallel lines are defined as lines that are always equidistant from each other and never meet. This definition applies to flat surfaces (such as the surface of a plane).

However, meridians are great circles on the sphere of the Earth. All great circles on a sphere, such as meridians, intersect at two points (the poles). Since meridians converge at the poles, they are not parallel in Euclidean geometry.

In the context of spherical geometry (which is more appropriate for Earth's surface), meridians are not parallel because they eventually intersect at the poles.

To summarize:

• Euclidean geometry (flat plane): Parallel lines do not meet.
• Spherical geometry (Earth's surface): Meridians (great circles) are not parallel because they intersect at the poles.

Let me know if you'd like more details about Euclidean vs. spherical geometry or how parallelism works in each!

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Follow-up Questions:

1. How do meridians and parallels differ in spherical geometry?
2. What is the definition of parallel lines in Euclidean geometry?
3. What is the difference between Euclidean and spherical geometry?
4. How are meridians and parallels used in navigation?
5. Can two great circles ever be parallel on a sphere?

Tip:

When working with spherical geometry, remember that lines (like meridians and parallels) are often not "straight" in the Euclidean sense, but are instead curved to match the curvature of the sphere.