Final answer:
Option (a) is the closest to a biconditional statement, stating if two lines are in the same plane and do not intersect, they are parallel. However, a true biconditional statement should also include the reverse condition, confirming that parallel lines must also not intersect and be in the same plane.
Step-by-step explanation:
The correct definition as a biconditional statement for two lines in the same plane that do not intersect being parallel lines is: If two lines are in the same plane and do not intersect, then they are parallel; and if two lines are parallel, then they are in the same plane and do not intersect. This definition ensures that both conditions are necessary and sufficient for lines to be parallel. The two lines not intersecting implies that they are parallel (the forward condition), and being parallel means that they will not intersect (the backward condition).
Looking at the options provided, none of them are perfect biconditional statements. However, the one that most closely represents a biconditional relationship is option (a), which states: If two lines are in the same plane and do not intersect, they are parallel. This option correctly addresses the forward condition of the biconditional relationship. To be completely accurate, it would need to be phrased to include the reverse condition as well.