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:

• Corresponding angles theorem: Compares angles in the same position relative to parallel lines and a transversal.
• Alternate interior angles theorem: Deals with angles between parallel lines and on opposite sides of the transversal.
• Vertical angles theorem: Focuses on angles opposite each other when two lines intersect.
• Alternate exterior angles theorem: Applies to angles outside the parallel lines and on opposite sides of the transversal.
• In this case, ∠2 and ∠6 are on opposite sides of the transversal \(c\) and inside the parallel lines \(a\) and \(b\), which is the definition of alternate interior angles.

Answer:

alternate interior angles theorem