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Discuss or reflect on why "in the same plane" is an important part of the definition. If you think in three dimensions, two lines can never intersect but also be not parallel. To demonstrate this, you can draw a line on one piece of paper, then draw a line on another piece of paper. Put one of the pieces of paper on a table or desk, and hold the second one above the first, parallel to it. You can rotate the second piece of paper and see that the two lines will never intersect as long as the planes (papers) stay parallel, but the lines are not always parallel to each other.
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