Two Column Proof of a TheoremDate: 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/ |
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