Question

the consecutive exterior angles theorem states, if two lines intersected by a transversal are parallel, then the consecutive exterior angles are supplementary. which of the following statements correctly states the converse of the consecutive exterior angles theorem, and correctly judges its validity? if consecutive exterior angles are supplementary, then the lines intersected by a transversal are parallel. this is valid. if consecutive exterior angles are supplementary, then the lines intersected by a transversal are not parallel. this is not valid. if consecutive exterior angles are congruent, then the lines intersected by a transversal are parallel. this is valid. if consecutive exterior angles are congruent, then the lines intersected by a transversal are not parallel. this is not valid.

Explanation:

Step1: Recall the Consecutive Exterior Angles Theorem

The original theorem states when lines are parallel, consecutive - exterior angles are supplementary.

Step2: Form the Converse

The converse flips the hypothesis and conclusion: if consecutive - exterior angles are supplementary, then lines are parallel.

Step3: Determine Validity

By geometric principles, when consecutive exterior angles are supplementary, the lines must be parallel, so it's valid.

Answer:

If two lines intersected by a transversal are parallel, then the consecutive exterior angles are supplementary. The converse of this is: If consecutive exterior angles are supplementary, then the lines intersected by a transversal are parallel. This converse statement is valid. So the answer is "If consecutive exterior angles are supplementary, then the lines intersected by a transversal are parallel. It is valid."