Question

in the given figure, which lines are parallel? justify your answer. determine the pairs of parallel lines. choose the correct answer below. a. hb||af by the converse of the vertical angles theorem b. hb||af by the converse of the alternate interior angles theorem c. ha||bf by the converse of the same - side interior angles postulate d. ha||bf by the converse of the corresponding angles theorem e. ha||bf by the converse of the alternate interior angles theorem help me solve this view an example get more help clear all

Explanation:

Step1: Recall angle - related parallel - line theorems

The vertical - angles theorem states that vertical angles are equal, but it doesn't directly prove lines are parallel. The corresponding - angles theorem says that if corresponding angles are equal, then the lines are parallel. The same - side interior angles postulate states that if same - side interior angles are supplementary, then the lines are parallel. The alternate interior angles theorem states that if alternate interior angles are equal, then the lines are parallel.

Step2: Analyze each option

We need to determine which pair of lines is parallel based on the correct theorem. Without seeing the figure, we assume the knowledge of angle relationships. If we consider the alternate interior angles formed by two lines and a transversal, when the alternate interior angles are equal, the lines are parallel.

Answer:

B. $\overleftrightarrow{HB}\parallel\overleftrightarrow{AF}$ by the Converse of the Alternate Interior Angles Theorem