Two lines are parallel if and only if they have the same slope. Two lines are perpendicular if the product of their slopes is -1. If neither of these conditions are met, the lines are nether parallel, or perpendicular.
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In two dimensions: They are parallel if their gradients are the same. They are perpendicular if the product of their gradients is -1. Otherwise they are neither. The nature of the question suggests that you have not yet studied lines in 3 or more dimensions.
Parallel
Perpendicular is when two lines cross... Parallel is when two lines never meet.... _____________ _____________ = PARALLEL LINES If they cross they are perpendicular, if they don't, they are parallel.
A rhombus has parallel lines but no perpendicular lines.
Right triangles have a set of perpendicular lines and no parallel lines.