Final answer:
In geometry, two lines are parallel if they will never intersect or cross each other. If two lines do intersect, like line n and m in the problem, they are not parallel by definition.
Step-by-step explanation:
The student is asking about the properties and relationships of lines in geometry. In the case presented, we have four lines: ℓ, m, n, and t. Line ℓ is not parallel to line m, and line n is constructed to be parallel to ℓ but also passing through the intersection of m and t. Because line n intersects m, they are not parallel.
Let's further dissect the information. Non-parallel lines are lines that meet or cross each other at some point. Two lines are said to be parallel if they never intersect and remain the same distance apart, no matter how far they are extended. In this scenario, line n is said to be parallel to line ℓ, meaning that they will never meet or cross. However, line n intersects line m, meaning they meet or cross at a certain point. Therefore, by definition, lines m and n are not parallel.
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