Question

given: lines a and b are parallel and line c is a transversal. prove: ∠2 is supplementary to ∠8 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

Explanation:

Step1: Recall Angle Theorems

When two parallel lines are cut by a transversal, alternate interior angles are congruent. Let's identify the angles: ∠2 and ∠6 are alternate interior angles (lines a || b, transversal c).

Step2: Match with Options

• Corresponding angles: Different position (e.g., ∠2 and ∠6 aren't corresponding).
• Vertical angles: ∠2 and ∠6 aren't vertical.
• Alternate exterior: ∠2 and ∠6 are interior, not exterior.
• Alternate interior angles theorem: States alternate interior angles are congruent when lines are parallel. So ∠6 ≅ ∠2 is by alternate interior angles theorem.

Answer:

alternate interior angles theorem