Proofs and ReasonsDate: 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/ |
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