Question

Given: a ∥ b and ∠1 ≅ ∠3
Prove: e ∥ f

Horizontal and parallel lines e and f are intersected by parallel lines a and b. At the intersection of lines a and e, the bottom left angle is angle 1. At the intersection of lines b and e, the uppercase right angle is angle 2. At the intersection of lines f and b, the bottom left angle is angle 3 and the bottom right angle is angle 4.

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

Answer:

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Answer 2

Answer:

The missing information in the paragraph is:

∠2 ≅ ∠3

Step-by-step explanation:

The alternate interior angles refers to those angles which are formed when a transversal cut the two parallel lines. They lie in the interior of the transversal and parallel lines.

The alternate exterior angles refers to those angles which are formed when a transversal cut the two parallel lines. They lie in the exterior of the transversal and parallel lines.

The parallel lines are those lines which do not intersect each other at any punt.

Here ∠2 and ∠3 are the alternate exterior angles.

Therefore, option (C) ∠2 ≅ ∠3is the correct option.

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