Answered

At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Given: l || m; ∠1 ∠3

Prove: p || q

Horizontal and parallel lines l and m are intersected by parallel lines p and q. At the intersection of lines l and p, the uppercase left angle is angle 1. At the intersection of lines q and l, the bottom right angle is angle 2. At the intersection of lines q and m, the uppercase left angle is angle 3.

Complete the missing parts of the paragraph proof.



We know that angle 1 is congruent to angle 3 and that line l is parallel to line m because
. We see that is congruent to by the alternate interior angles theorem. Therefore, angle 1 is congruent to angle 2 by the transitive property. So, we can conclude that lines p and q are parallel by the

.

Sagot :

akposevictor

The parts that are missing in the proof are:

It is given

∠2 ≅ ∠3

converse alternate exterior angles theorem

What is the Converse of Alternate Exterior Angles Theorem?

The theorem states that, if two exterior alternate angles are congruent, then the lines cut by the transversal are parallel.

∠1 ≅ ∠3 and l║m because we are: given

By the transitive property,

∠2 and ∠3 are alternate interior angles, therefore, they are congruent to each other by the alternate interior angles theorem.

Based on the converse alternate exterior angles theorem, lines p and q are proven to be parallel.

Therefore, the missing parts pf the paragraph proof are:

  • It is given
  • ∠2 ≅ ∠3
  • converse alternate exterior angles theorem

Learn more about the converse alternate exterior angles theorem on:

https://brainly.com/question/17883766

#SPJ1

View image akposevictor
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.