$$In the context of the Law of Sines $\mathrm{Law} \mathrm{of} \mathrm{Sines}$ and triangle geometry, if two lines (such as transversals or sides) are not parallel, which types of angles remain congruent?

• A. $$Only vertical angles remain congruent
• B. $$Alternate interior angles remain congruent
• C. $$Corresponding angles remain congruent
• D. $$No angles remain congruent

Answer: (A)

Verified step by step guidance

1. Recall that when two lines are cut by a transversal, certain angle pairs can be congruent depending on whether the lines are parallel or not.
2. Understand that alternate interior angles and corresponding angles are congruent only if the two lines are parallel.
3. Recognize that vertical angles are formed by two intersecting lines and are always congruent regardless of whether the lines are parallel or not.
4. Since the problem states the two lines are not parallel, eliminate alternate interior angles and corresponding angles as congruent pairs.
5. Conclude that only vertical angles remain congruent when two lines are not parallel.