Question

In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving that lines l and m are parallel. Angles 1 and 2 are supplementary by definition. Submit the entire proof to your instructor.
Given: ∠1 and ∠2 are supplementary angles Prove: l || m 



STATEMENT                                                   REASON 
1.∠1 and ∠2 are supplementary angles           1. Given 
2. m∠1 + m∠2 = 180°                                       2. 
3. ∠1 and ∠3 are supplementary angles          3. Exterior sides in opposite rays 
4.                                                                      4. 
5. m∠1 + m∠2 = m∠1 + m∠3                           5.
6.                                                                      6. 
7. l || m                                                             7.

Answer 1

Answer:

See the proof.

Step-by-step explanation:

Statement                                                               Reason

1.∠1 and ∠2 are supplementary angles     ---           Given  

2. m∠1 + m∠2 = 180°     ---                  Linear pair, they are supplementary                                

3. m∠1  and m∠3 are supplementary angles --  m∠1 + m∠3= 180

                                                                              (Supplementary angles add upto 180 degrees)  

4.  m∠1 and m∠3           ------                                 Exterior sides in opposite rays

5.   m∠1 + m∠2 = m∠1 + m∠3  ------                       Transitive property  

6.    m∠2 = m∠3                     --------------                Subtraction  property

7.   l || m  ------------- If two lines are cut by transversal the alternative interior

                               angles are the same, then the lines are paralle.

Thank you.