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

Answer 1

`\angle 1\cong \angle 2`

Explanation:

We have to find the missing statement in the given proof.

Angle 1 is congruent to angle 3

Given

Line a is parallel to line b

Given

`\angle 1\cong \angle 2`

By using alternate exterior angles theorem.

`\angle 2\cong \angle 3`

Therefore,
`\angle 2\cong \angle 3`

By the transitive property of congruence.

So, we can conclude that lines e and f are parallel by the converse alternate exterior angles theorem.

Answer:
`\angle 1\cong \angle 2`

Answer 2

∠1 ≅ ∠2

Explanation:

The transitive property says that if ∠1 ≅ ∠3 and ∠1 ≅ ∠2, then ∠2 ≅ ∠3. The missing part of this statement in the paragraph is ∠1 ≅ ∠2.