Given: m ∠3 = m ∠4 to prove: ∠1, ∠2 are supplementary

Statement                                           Reason

1) m<3 = m<4  :                                    (Given).

2) <2 and <3 are supplementary :     (Linear pair).

3) m<2 + m<3. =180. :                          Definition of supplementary angles.

4) m<2 + m<4. = 180. :                         Substitution.

5) m<1 = m<4. :                                    Opposite angles equal.

6) m<2 + m<1 = 180. :                          Substitution.

7) <1, <2 are supplementary :       Definition of consecutive exterior angles.

∠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.