Question

determine the pairs of parallel lines. choose the correct answer below.
a. cd∥mn by the converse of the same - side interior angles theorem
b. cd∥mn by the converse of the same - side interior angles postulate
c. cd∥mn by the converse of the alternate exterior angles theorem
d. cd∥mn by the converse of the corresponding angles theorem
e. cd∥mn by the alternate interior angles theorem
f. cd∥mn by the alternate interior angles postulate

Explanation:

Step1: Recall parallel - lines theorems

When two lines are parallel, different angle - related theorems apply. The Same - Side Interior Angles Theorem states that if two parallel lines are cut by a transversal, the same - side interior angles are supplementary. Its converse is used to prove that two lines are parallel when the same - side interior angles are supplementary.

Step2: Analyze the options

The Alternate Interior Angles Theorem and its converse deal with alternate interior angles. The Alternate Exterior Angles Theorem and its converse deal with alternate exterior angles. The Corresponding Angles Theorem and its converse deal with corresponding angles. But in the context of proving parallel lines using same - side interior angles, we use the Converse of the Same - Side Interior Angles Theorem.

Answer:

A. $\overleftrightarrow{GM}\parallel\overleftrightarrow{HC}$ by the Converse of the Same - Side Interior Angles Theorem