Proofs and Reasons

Date: 01/03/99 at 19:31:12
From: Maggy
Subject: Proofs and Reasons

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
               /   \
             /       \
           /           q
         p               \
       /                   \
     a-----------------------b

      STATEMENT                REASON

      1. AC > BC and AP = BQ   Given
      2. AC-AP = PC            Subtraction property of inequality
      3. BC-BQ = QC            Subtraction property of inequality
      4. PC = QC               Substitution Property

This is what I have for my answer to the question. My question is: are 
steps 2 and 3 correct? I don't think they are but I couldn't find or 
think of any other way to do it.

Date: 01/04/99 at 08:31:24
From: Doctor Jerry
Subject: Re: Proofs and Reasons

Hi Maggy,

From the diagram, I think you want me to assume that P lies between A 
and C and Q lies between C and B.

I wouldn't want to say statement 2 is wrong. However, to say that 
AC - AP = PC is the "subtraction property of inequality" doesn't 
compute with me. I think I'd arrange matters this way:

   AC > BC             given

   AC - AP > BC - BQ, (the same number can be subtracted from both 
                       sides of an inequality)
   PC > QC

I don't know what to call this last step. It's a geometric operation, 
not a property of inequalities.

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