Two Column Proof of a Theorem

Date: 08/12/98 at 15:39:41
From: Brandon Pendrys
Subject: Two Column Proof of a Theorem

I homeschool, and this question really has me stuck.

Q. Write a two-column proof for the following theorem. Give numbered
   statements with reasons.

   Given: AC > BC and AP = BQ
   To Prove: PC > QC

                   c
                   ^
                /    \
             p/       \q
            /          \
         a/_____________\b

I Set my proof up like this so far:

         STATEMENT      |      REASON
----------------------------------------------------
1. AC>BC and AP=BQ      |   1. Given
2.                      |   2.

Now how do I know what to do next and how do I figure my reason?

Thank you for your time.
Brandon Pendrys

Date: 08/12/98 at 16:30:58
From: Doctor Rob
Subject: Re: Two Column Proof of a Theorem

The next step is "AC = AP + PC" and the reason is "The whole is the sum 
of its parts." The following step is "BC = BQ + QC" with the same 
reason.

Next substitute from steps 2 and 3 into the inequality in step 1, with
the reason "Substitution."  Finally subtract AP = BQ (step 1) from both
sides of the inequality in step 4, reason, "Equals subtracted from 
unequals are unequal in the same sense," (or whatever wording your 
teacher thinks reflects the correctness of this operation).  

Finally, simplify the resulting inequality to get your answer.

- Doctor Rob, The Math Forum
  http://mathforum.org/dr.math/