Cumulative Standards Review
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Think about the Converse of the Alternate Interior Angles Theorem.
B
To find the answer, let's go through each option one at a time.
Although these corresponding angles are supplementary, 85+95=180, we can clearly see that the lines are not parallel. Therefore, we cannot use this relationship to prove that the lines are parallel.
Let's recall what the Converse of the Alternate Interior Angles Theorem says. If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel. According to this theorem, we can always prove that lines are parallel using congruent alternate interior angles.
Vertical angles are formed by two intersecting lines. Parallel lines never intersect. Therefore, we cannot use congruent vertical angles to prove that the lines are parallel.
Let's use the Converse of the Same-Side Interior Angles Postulate this time. If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel. As we can see, the angles should be supplementary, not congruent. If both same-side interior angles are 90^(∘), then they are congruent and supplementary at the same time. In any other case, when the angles are congruent, it does not help us to prove that the lines are parallel. Let's look at an example.
These angles are congruent, but the lines are clearly not parallel. We cannot use this relationship to prove that the lines are parallel.
The only option that can be used is congruent alternate interior angles, which corresponds to Option B.