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:

To find the missing reason for \( \angle 6 \cong \angle 2 \), we analyze the angles formed by parallel lines \( a \parallel b \) and transversal \( c \). \( \angle 2 \) and \( \angle 6 \) are corresponding angles (they occupy the same relative position at each intersection where a straight line crosses two others). The Corresponding Angles Theorem states that if two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent. So the reason for \( \angle 6 \cong \angle 2 \) is the corresponding angles theorem.

Answer:

A. corresponding angles theorem