A student claims that if any two planes that do not intersect

are parallel, then any two lines that do not intersect should
also be parallel. How do you respond?

The issue is what do you answer? I will be happy to critique your response.

I get the feeling you are answer grazing.

yes because they never touch

To respond to the student's claim, you can explain that their statement is incorrect. The relationship between planes and lines is not the same.

Here's a more detailed explanation:

1. Firstly, let's understand the definition of parallel lines: Two lines are parallel if they lie in the same plane and do not intersect, meaning they maintain a constant distance from each other.

2. Now, consider two planes in three-dimensional space. A plane is a flat surface that extends infinitely in all directions. If two planes do not intersect, they can be considered parallel.

3. However, lines are fundamentally different from planes. A line is a one-dimensional object that extends infinitely in two opposite directions. Unlike planes, lines cannot intersect only in the context of parallelism.

4. It's important to note that parallelism is not automatically established when lines don't intersect. Two lines may not intersect but still not be parallel. For example, think about two skew lines - they are two non-intersecting lines that do not lie on the same plane and are not parallel.

In conclusion, the claim that if two planes are parallel, then any two lines that do not intersect are also parallel is incorrect. The relationship between planes and lines is distinct, and two lines must lie in the same plane and not intersect to be considered parallel.