Question

3.8.6 check your understanding
complete the paragraph proof shown.
given: ∠1≅∠8
prove: ∠2≅∠7
since it is given that ∠1≅∠8 and ∠1 and ∠8 are alternate exterior angles formed by two lines intersected by a transversal, then
therefore, ∠2≅∠7 because when two parallel lines are intersected by a transversal, then alternate interior angles are congruent.
○ b||k
○ b||w
○ k||n
○ w||n

Explanation:

Step1: Recall angle - parallel line relationship

If alternate exterior angles are congruent, then the lines are parallel. Since $\angle1\cong\angle8$ and they are alternate exterior angles formed by lines $b$ and $k$ intersected by a transversal, we can conclude about the parallel - ness of the lines.

Step2: Identify parallel lines

The congruence of alternate exterior angles $\angle1$ and $\angle8$ implies that $b\parallel k$.

Answer:

$b\parallel k$