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

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

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

Answer

Explanation:

Step1: Identify angle - pair relationship

We know that when two parallel lines are cut by a transversal, we need to find the reason for $\angle6\cong\angle2$.

Step2: Recall angle - congruence theorems

$\angle6$ and $\angle2$ are corresponding angles. The corresponding angles theorem states that when two parallel lines are cut by a transversal, corresponding angles are congruent.

Answer:

corresponding angles theorem