Question

answer attempt 1 out of 10
if ∠15≅∠8 what lines are parallel? c&d
theorem: corresponding angles theorem
if ∠13≅∠9 what lines are parallel? none
theorem: none
if ∠6≅
theorem: corresponding angles theorem
alternate interior angles theorem
alternate exterior angles theorem
consecutive interior angles theorem
if ∠6&∠
el? c&d
theorem: consecutive interior angles theorem

Explanation:

Step1: Recall angle - parallel line relationships

When two lines are cut by a transversal, if corresponding angles are congruent, the lines are parallel. Given $\angle15\cong\angle8$, by the Corresponding Angles Theorem, the lines are parallel. For $\angle13$ and $\angle9$, they do not fit the angle - pair relationships (corresponding, alternate interior, alternate exterior, consecutive interior) that imply parallel lines, so no lines are parallel.

Step2: Analyze $\angle6$ cases

If considering the relationship of $\angle6$ to other angles to determine parallel lines, different angle - pair theorems can be applied. The Corresponding Angles Theorem states that if corresponding angles are congruent, the lines are parallel; the Alternate Interior Angles Theorem states that if alternate interior angles are congruent, the lines are parallel; the Alternate Exterior Angles Theorem states that if alternate exterior angles are congruent, the lines are parallel; and the Consecutive Interior Angles Theorem states that if consecutive interior angles are supplementary, the lines are parallel.

Answer:

If $\angle15\cong\angle8$, the lines are parallel by the Corresponding Angles Theorem. If $\angle13\cong\angle9$, no lines are parallel. For $\angle6$, depending on its relationship to other angles, different theorems (Corresponding Angles Theorem, Alternate Interior Angles Theorem, Alternate Exterior Angles Theorem, Consecutive Interior Angles Theorem) can be used to determine parallel lines.