Final Answer:
The given information, ∠1 ≅ ∠8, proves that lines a and b are parallel.
Step-by-step explanation:
The Converse of the Alternate Exterior Angles Theorem states that if alternate exterior angles are congruent, then the lines are parallel. In this case, ∠1 and ∠8 are alternate exterior angles. When ∠1 ≅ ∠8, it implies that the corresponding alternate exterior angles are congruent. By the Converse of the Alternate Exterior Angles Theorem, this establishes that lines a and b are parallel.
To elaborate, the Alternate Exterior Angles Theorem asserts that when two parallel lines are intersected by a transversal, the pairs of alternate exterior angles formed are congruent. Mathematically, if line a is parallel to line b, then ∠1 ≅ ∠8. Conversely, if ∠1 ≅ ∠8, it implies that the lines are parallel. This can be verified by considering the transversal and the corresponding alternate exterior angles formed. The equality of these angles demonstrates the parallel nature of the lines.
In summary, the given congruence of ∠1 and ∠8 serves as evidence for the parallelism of lines a and b according to the Converse of the Alternate Exterior Angles Theorem. This logical connection relies on the fundamental geometric principles governing parallel lines and their corresponding angle relationships.