Question

in the given figure, which lines are parallel? justify your answer. determine the pairs of parallel lines. choose the correct answer below. a. mf∥on by the converse of the vertical angles theorem b. mf∥on by the converse of the alternate interior angles theorem c. mg∥fn by the converse of the alternate interior angles theorem d. mo∥fn by the converse of the corresponding angles theorem e. mo∥fn by the converse of the same - side interior angles postulate

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 two lines are parallel. Looking at the figure and the options, we need to identify the correct pair of parallel lines based on this theorem. Option C mentions \(MO\parallel PN\) by the converse of the alternate - interior angles theorem.

Answer:

C. \(MO\parallel PN\) by the Converse of the Alternate Interior Angles Theorem