document.write( "Question 576401: how do you do 2 column geometry proofs ? \n" ); document.write( "
Algebra.Com's Answer #369987 by richard1234(7193)\"\" \"About 
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There is no \"set\" method on how to prove something. You have to decide which approach to take for a certain problem, and stick to it if it works. Once you have proved it, write out each statement on the left hand column, and write out the reason for each statement on the right hand column (i.e. why is this true?).\r
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\n" ); document.write( "\n" ); document.write( "However, two-column proofs have several pitfalls, and they are rarely used by professional mathematicians. This is mostly because difficult proofs that take several pages in an essay would definitely take much more space in two-column format. Additionally, certain proof techniques or methods(e.g. WLOG assumptions*, contradiction) are more difficult to put into a two-column format. Nevertheless, they are still useful when learning proofs, since you will be able to show *why* something must be true. Once you become more experience with writing proofs, you will most probably switch to writing proofs in an essay rather than two column.\r
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\n" ); document.write( "\n" ); document.write( "*The other tutor stated never to assume anything. This is true up to a certain extent (e.g. NEVER assume a right triangle is a 45-45-90 or 30-60-90 triangle unless you can prove it; I see many students make this faulty assumption for no apparent reason whatsoever). There are certain other problems where you have to make an assumption. For example, if you were asked to find all solutions (x,y,z) of real numbers satisfying\r
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\n" ); document.write( "\n" ); document.write( "In this case, it is perfectly valid to assume that since the equations are symmetric. It may or may not lead to a complete solution; I'll let you figure that out.\r
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