Question - Determining Parallel Lines Using Alternate Interior Angles
Solution:
The image shows two lines cut by a transversal, with two angles labeled as $$ m \angle 4 $$ and $$ m \angle 7 $$. We are told that $$ m \angle 4 = m \angle 7 $$. This means angle 4 and angle 7 are congruent.Using this information, we can determine which lines are parallel. Congruent corresponding angles, which occur when a transversal crosses two parallel lines, imply that the lines are indeed parallel. In this case, angle 4 and angle 7 are alternate interior angles. According to the Alternate Interior Angles Theorem, if alternate interior angles are congruent, then the lines are parallel.So, the correct answer is:\[ \bar{t} || \bar{m}, \text{ by the Converse of the Alternate Interior Angles Theorem.} \]This is the third option in the list provided in the image.
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