Writing a Proof

[stupidmathgirl]

I know how to write poofs and all, but I don't understand how to even start with this problem.

Write a two-column proof that angle 2 is congruent to angle 3. Given: Angle 1 and angle 4 are congruent. (http://i54.tinypic.com/ao89ic.jpg)

I feel so stupid; I'm sorry if this seems simple to you. Thanks for the help in advanced!

 

[akoaysigod]

I don't know what you mean by two column proof but are you missing information about lines a and b? Because lines a and b have a special property which make angles 2, 3 congruent if angles 1, 4 are congruent.

 

[stupidmathgirl]

Oh yes, lines a and b are parallel. I forgot to mention that. And a two column proof is where you say something like

∠1 ≅ ∠4 | Given
∠4 ≅ ∠3 | Definition of supplementary angles

It's like a proof but you divide it into two columns instead of writing it in a paragraph.

 

[Mrspi]

I don't know what you mean by two column proof but are you missing information about lines a and b? Because lines a and b have a special property which make angles 2, 3 congruent if angles 1, 4 are congruent.

Since you've indicated that lines a and b are parallel, you can make use of the fact that each pair of interior angles on the same side of the transversal are supplementary. That's a theorem that you should have already proved if you are studying angle relationships when a pair of parallel lines are cut by a transversal.

I'd start your proof like this:

1.  lines a and b are parallel               1.  Given
2.  <1 and <2 are supplementary              2.  If two lines are parallel, then
     <3 and <4 are supplementary                each pair interior <s same 
                                                  side of transversal suppl.

Now, you are given a pair of congruent angles, and you should have a theorem which says that supplements of congruent angles are congruent...this should allow you to complete the proof in about 2 more statements.