Question

Given: Lines a and b are parallel and line c is a transversal.
Prove: Angle2 is supplementary to Angle8

Horizontal and parallel lines a and b are cut by transversal c. On line a where it intersects line c, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 2, 4, 3. On line b where it intersects line c, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 5, 6, 8, 7.
What is the missing reason in the proof?

Statement Reason
1. a || b, c is a transversal 1. given
2. ∠6 ≅ ∠2 2. ?
3. m∠6 = m∠2 3. def. of congruent
4. ∠6 is supp. to ∠8 4. def. of linear pair
5. ∠2 is supp. to ∠8 5. congruent supplements theorem
corresponding angles theorem
alternate interior angles theorem
vertical angles theorem
alternate exterior angles theorem

Answer 1

Corresponding angles theorem.

Since a ∥ b and c is a transversal, ∠2 and ∠6 are corresponding angles, so they are congruent.