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In Euclidean geometry parallel lines are always the same distance apart.

In non-Euclidean geometry parallel lines are not what we think of a parallel. They curve away from or toward each other.

Said another way, in Euclidean geometry parallel lines can never cross. In non-Euclidean geometry they can.

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Q: What is the difference between Euclidean Geometry and non-Euclidean Geometry?
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