The reasons that completes the Corresponding Angles Theorem proof are:
1. k || l - Given
2. ∠8 ≅ ∠4 - Alternate angles theorem
3. ∠2 ≅ ∠8 - Vertically Opposite Angles Theorem
4. ∠2 ≅ ∠4 - Corresponding angles Theorem.
1. Parallel Lines Theorem: If a transversal intersects two parallel lines, then corresponding angles are congruent, alternate angles are congruent, and interior angles are supplementary.
2. Alternate Angles Theorem: If two parallel lines are intersected by a transversal, then alternate interior angles are congruent.
3. Vertically Opposite Angles Theorem: In an intersecting line configuration, vertically opposite angles are congruent.
4. Corresponding Angles Theorem: If a transversal intersects two parallel lines, then corresponding angles are congruent.