We appreciate your visit to 7 8 points For the following theorem draw a picture and use the picture to write the given and prove statement If two lines are. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
If two lines are cut by a transversal, and the exterior angles on the same side of the transversal add up to 180 degrees, then those lines are parallel, as per the converse of the Alternate Exterior Angles Theorem.
The given theorem states that if two lines are cut by a transversal in such a way that the exterior angles on the same side of the transversal are supplementary (add up to 180 degrees), then these lines are parallel.
For prove this theorem, we can start by drawing a picture.
Let's draw two lines, labeled line l and line m, and a transversal, labeled t, that intersects both lines.
Two lines l and m are cut by a transversal t.
Prove: If the exterior angles on the same side of the transversal are supplementary, then lines l and m are parallel.
In the picture, we can label the exterior angles as ∠1 and ∠2.
These angles are located on the same side of the transversal t.
According to the given information, if ∠1 and ∠2 are supplementary, meaning that they add up to 180 degrees, then we need to prove that lines l and m are parallel.
For prove this, we can use the converse of the Alternate Exterior Angles Theorem.
This theorem states that if two lines are cut by a transversal and the alternate exterior angles are congruent (equal), then the lines are parallel.
In this case, we are given that the exterior angles are supplementary, which means they are equal to 180 degrees together.
Using this information, we can conclude that ∠1 and ∠2 are congruent.
Therefore, by the converse of the Alternate Exterior Angles Theorem, lines l and m are parallel.
Hence, if two lines are cut by a transversal and the exterior angles on the same side of the transversal are supplementary (add up to 180 degrees), then these lines are parallel.
This can be proven by applying the converse of the Alternate Exterior Angles Theorem.
To know more about transversal visit
https://brainly.com/question/33245447
#SPJ11
Thanks for taking the time to read 7 8 points For the following theorem draw a picture and use the picture to write the given and prove statement If two lines are. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
