Question

in the given figure, which lines are parallel? justify your answer
a. ke||kn by the converse of the alternate interior angles theorem
b. ng||kn by the converse of the same - side interior angles postulate
c. ng||eg by the converse of the alternate exterior angles theorem
d. ke||eg by the converse of the alternate interior angles theorem
e. ke||ng by the converse of the same - side interior angles theorem
f. kn||eg by the converse of the corresponding angles theorem
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Explanation:

The Alternate Interior Angles Theorem states that if two parallel lines are cut by a transversal, then the alternate - interior angles are congruent. Conversely, if alternate - interior angles are congruent, then the lines are parallel. In the given problem, we are looking for a justification for parallel lines based on angle relationships. The Alternate Interior Angles Theorem is relevant here as it provides a way to determine parallelism based on angle congruence.

Answer:

A. KE||KN by the Converse of the Alternate Interior Angles Theorem