Question

in the given figure, which lines are parallel? justify your answer. determine the pairs of parallel lines. choose the correct answer below. a. fg||db by the converse of the alternate interior angles theorem b. fd||gb by the converse of the vertical angles theorem c. fg||db by the converse of the same - side interior angles postulate d. fg||db by the converse of the corresponding angles theorem e. fd||gb by the converse of the alternate interior angles theorem

Explanation:

The Converse of the Alternate Interior Angles Theorem states that if two lines are cut by a transversal and the alternate - interior angles are congruent, then the lines are parallel. In the given figure, if the alternate - interior angles formed by lines FG and DB with a transversal are congruent, then FG and DB are parallel. There is no such condition met for the other pairs of lines and the other theorems (Vertical Angles Theorem is not used to prove parallel lines, and there is no indication of same - side interior angle or corresponding angle congruence for the given pairs).

Answer:

A. FG||DB by the Converse of the Alternate Interior Angles Theorem