Given: a ∥ b and ∠1 ≅ ∠3 prove: e ∥ f 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

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

the answer is b.)

< 1=< 2