They would 'intersect'. ('cross', have one point in common)
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You would get a set of angles whose interrelationships would be more complex.
Otherwise nobody would know what was meant by parallel lines!
Parallel lines would always lie in the same plane. They would need to be skew lines.
The answer would be parallel lines these lines never meet or cross each other.
Four parallel lines would not correspond to any of the commonly taught shapes. Two pairs of parallel lines would be characteristic of the square, rhombus, rectangle, and parallelogram