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, line \(a\parallel b\) and transversal \(e\) (or \(f\)) is used.

Step2: Analyze the angles

Since \(a\parallel b\) and considering the transversal (say \(e\) and \(f\) - related to the angles), by alternate exterior angles theorem, \(\angle1\cong\angle2\) (because \(a\) and \(b\) are parallel and they are alternate exterior angles with respect to the transversal that forms \(\angle1\) and \(\angle2\)).

Answer:

\(\angle1\cong\angle2\)