Question

for #9 - 12, determine if a || b or not. justify your ans
9.
10.
11.
12.

Explanation:

Step1: Recall the Alternate Exterior Angles Theorem

If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent. Conversely, if the alternate exterior angles are congruent, then the two lines are parallel.

Step2: Analyze the angles in problem 9

In problem 9, the two angles marked \(71^{\circ}\) are alternate exterior angles. Since they are equal (\(71^{\circ}=71^{\circ}\)), by the Alternate Exterior Angles Theorem, \(a\parallel b\).

Step3: Analyze the angles in problem 11

In problem 11, the two angles marked \(102^{\circ}\) are alternate exterior angles. Since they are equal (\(102^{\circ}=102^{\circ}\)), by the Alternate Exterior Angles Theorem, \(a\parallel b\).

Answer:

For problem 9: \(a\parallel b\) because the alternate exterior angles (\(71^{\circ}\) each) are congruent.
For problem 11: \(a\parallel b\) because the alternate exterior angles (\(102^{\circ}\) each) are congruent.