Question 576401: how do you do 2 column geometry proofs ?
Found 2 solutions by solver91311, richard1234:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
In column 1, write what you are given. In column 2, state the reason for the statement in column 1 as "Given"
In column 1, write some statement that follows from the givens. In column 2, states the reason for the new statement by identifying the applicable Postulate, Definition, or Theorem.
Continue writing new statements and supporting them with either Postulate, Definition, Theorem, or Given until you are able to state what it is you started out to prove in the first place.
Never assume ANYTHING. You have to be able to conclusively prove EVERY statement you make. Some teachers are more rigorous than others. For example, in some Geometry classes you can use the ideas of congruence of angles and the equality of angle measures interchangeably. Other teachers/instructors/professors will require that knowing two angles are congruent is insufficient to be able to use the equality of their measures without the intermediate step of saying that the measures are equal because of the definition of congruence.
"But how do I know what statements to make?" Use your imagination and logic to derive a strategy based on everything you have learned previously, then follow your strategy step by step. Every proof is different, so there is no generic answer to "How do I do proofs." Sorry about that, but the whole purpose of studying Geometry is to teach you how to creatively solve problems based solely on what you already know and extend that to what you are trying to find out. The only way to be successful is to practice the art and spend a good deal of time at it. Enjoy.
John
My calculator said it, I believe it, that settles it
Answer by richard1234(7193)  (Show Source):
You can put this solution on YOUR website! 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?).
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.
*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
(1)
(2)
(3)
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.
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