Question

in the given figure, which lines are parallel? justify your answer. determine the pairs of parallel lines. choose the correct answer below. a. ba∥em by the converse of the corresponding angles theorem b. be∥ea by the converse of the alternate exterior angles theorem c. be∥ea by the converse of the alternate interior angles theorem d. be∥ea by the converse of the same - side interior angles theorem

Explanation:

Step1: Recall angle - related parallel - line theorems

When two parallel lines are cut by a transversal, different angle - relationships are formed. The converse of the corresponding angles theorem states that if corresponding angles are congruent, then the lines are parallel. In the given figure, we need to identify the theorem used to determine parallel lines based on angle congruence.

Step2: Analyze the options

The converse of the alternate interior angles theorem says that if alternate interior angles are congruent, then the lines are parallel. The converse of the alternate exterior angles theorem says that if alternate exterior angles are congruent, then the lines are parallel. The converse of the same - side interior angles postulate says that if same - side interior angles are supplementary, then the lines are parallel.

Step3: Match with the figure

Without seeing the specific angle - pair in the figure, we assume that if we are using the fact that a pair of corresponding angles are congruent to prove parallel lines, we use the converse of the corresponding angles theorem.

Answer:

A. By the Converse of the Corresponding Angles Theorem