Question

we know that angle 1 is congruent to angle 3 and that line a is parallel to line b because they are given. we see that ____________ by the alternate exterior angles theorem. therefore, angle 2 is congruent to angle 3 by the transitive property. so, we can conclude that lines e and f are parallel by the converse alternate exterior angles theorem. which information is missing in the paragraph proof?
∠2 ≅ ∠4
∠1 ≅ ∠2
∠2 ≅ ∠3
∠1 ≅ ∠4

Explanation:

Step1: Recall alternate exterior angles theorem

When two parallel lines are cut by a transversal, alternate exterior angles are congruent. Here, lines \(a\) and \(b\) are parallel. The transversal gives \(\angle1\) and \(\angle2\) as alternate exterior angles.

Step2: Apply the theorem

By the alternate exterior angles theorem, if two parallel lines (\(a\) and \(b\)) are cut by a transversal, then \(\angle1\cong\angle2\).

Answer:

\(\angle1\cong\angle2\) (the second option)