The difference between parallel lines and non-parallel lines that are cut by a transversal is that once the parallel lines are cut, their corresponding angles are congruent. Non-parallel lines don't necessarily have congruent corresponding angles. For example, in the picture in the top left, angles 4 and 5 are congruent but in the top right, angles 5 and 3 aren't congruent. Stay Classy!
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