Given: WX || YZ, ?2??3 Prove: WY || YZ

Question

I need a two column proof for this. With reasoning and citation.

Answer 1

Dear Selma,

     Hello, the Given is correct.  However, I believe that you mean the following for the "Prove:  WY ll XZ.   Draw the picture, and you will see that you can't prove the other.

 

 

____Statements_________l_______               Reasons_________________________

 

1.  WX ll YZ                                                         1.  Given

 

2.  Line Wy  and line XZ  are transversals.                      2.  Construct the lines.

 

3.  ∠A, ∠B, ∠C, ∠D are interior angles                  3.  When transversals intersect ll lines, angles are formed.

 

4.  ∠A + ∠B= 180º                                              4.  Definition of a straight angle

    

    ∠C + ∠D=180º

 

5.  m∠A=m∠C, and m∠B=m∠D                           6.   Alternate interior angles are equal.

 

6.  m∠C + m∠B= 180º                                       7.  Substitution

     m∠A + m∠D=180º

 

7.  Therefore, line WY ll line XZ                            8.   definition of parallel lines

 

Citations can be found by looking up properties of parallel lines cut by transversals.