Difference Between Parallel and Non-Parallel Lines Cut by a Transversal

  A pair of parallel lines cut by a transversal would follow and apply to the theorems. Non-Parallel lines would not have congruent angles in the same places the theorem suggests, and would not show the same results parallel segments would.

Above is an example of parallel lines cut by a transversal, following the theorems and staying consistent.

To the right is a non-parallel line pair cut by a transversal. The angles, which should be congruent or supplementary to each other, are not due to false angle measurements. Angle 1 is clearly not the same measure as angle 5, which would follow the corresponding angle postulate.