Question

1. a pair of parallel lines is intersected by a transversal. select each statement that can be used to show that ∠2 is congruent to ∠8. □ ∠2 and ∠8 are vertical angles, so ∠2 is congruent to ∠8. □ ∠2 and ∠8 are alternate interior angles, so ∠2 is congruent to ∠8. □ ∠2 and ∠8 are alternate exterior angles, so ∠2 is congruent to ∠8. □ ∠2 and ∠6 are corresponding angles, and ∠6 and ∠8 are vertical angles, so ∠2 is congruent to ∠8. □ ∠2 and ∠4 are vertical angles, and ∠4 and ∠8 are corresponding angles, so ∠2 is congruent to ∠8.

Explanation:

Step1: Recall angle - pair relationships

When two parallel lines are intersected by a transversal:

• Vertical angles are congruent. $\angle2$ and $\angle4$ are vertical angles, but this doesn't directly relate $\angle2$ and $\angle8$.
• Corresponding angles are congruent. But $\angle2$ and $\angle8$ are not corresponding angles.
• Alternate - interior angles are congruent. But $\angle2$ and $\angle8$ are not alternate - interior angles.
• Alternate - exterior angles are congruent. $\angle2$ and $\angle8$ are alternate - exterior angles.

Step2: Determine the correct relationship

Since $\angle2$ and $\angle8$ are alternate - exterior angles, by the property of parallel lines cut by a transversal, $\angle2\cong\angle8$.

Answer:

$\angle2$ and $\angle8$ are alternate exterior angles, so $\angle2$ is congruent to $\angle8$.