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Which of the following are true biconditional statements based on the theorems about parallel lines in Section 3.2 and the converses of those theorems in Section 3.3? Select all that apply.

A. Two lines cut by a transversal are parallel if and only if the corresponding angles are supplementary.

B. Two lines cut by a transversal are parallel if and only if the corresponding angles are congruent.

C. Two lines cut by a transversal are parallel if and only if the alternate exterior angles are supplementary.

Answer :

Final answer:

The true biconditional statements based on the theorems about parallel lines and the converses of these theorems are: two lines cut by a transversal are parallel if and only if the corresponding angles are congruent.

Explanation:

Within the context of theorems about parallel lines and the converses of these theorems, the correct and true biconditional statements are:

  • C. Two lines cut by a transversal are parallel if and only if the corresponding angles are congruent.
  • D. Two lines cut by a transversal are parallel if and only if the corresponding angles are congruent.

This means that if two lines are cut by a transversal, they are parallel only in the situation that corresponding angles are the same (congruent). If corresponding angles are congruent, this would automatically mean that the two lines are parallel. The other statements are incorrect as they suggest that corresponding angles and alternate exterior angles are supplementary, which would add up to 180 degrees, and not congruent (equal) as the true biconditional statement suggests.

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