Question

which pair of statements would prove that b || a and c || e? ∠2≅∠8 ; ∠6 is supplementary to ∠5 ∠5≅∠1 ; ∠2≅∠1

Explanation:

Step1: Recall parallel - line postulates

For two lines to be parallel, we use angle - relationships such as corresponding angles, alternate interior angles, and same - side interior angles.

Step2: Analyze corresponding angles

If $\angle5\cong\angle1$, then $b\parallel a$ because $\angle5$ and $\angle1$ are corresponding angles. When corresponding angles are congruent, the two lines are parallel.

Step3: Analyze supplementary angles

If $\angle2\cong\angle1$, then we know that $\angle2$ and $\angle5$ are also congruent (since $\angle5\cong\angle1$). Also, if $\angle6$ is supplementary to $\angle5$, and we consider the relationship between the lines $c$ and $e$, we can use the fact that same - side interior angles or other angle relationships related to parallel lines. When $\angle5\cong\angle1$ and $\angle2\cong\angle1$, we have consistent angle relationships for parallel lines.

Answer:

$\angle5\cong\angle1;\angle2\cong\angle1$