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Being 'Parallel' , they only meet at INFINITY.
Non-intersecting lines in 3-D space may be parallel but need not be.
All of the three sides of a triangle can be parts of parallel lines; it's just that no two of them can be parallel with each other. They can be parallel to some other line(s). In plane geometry parallel lines cannot form the sides of a common triangle.
Parallel lines have the same slope.
A rectangular prism has 3 sets of 4 parallel lines and 24 angles.