Question 464262: Hi, I am a student who is taking Geometry for the first time at a summer Geometry Course. As I have never learned geometry before, I am having a difficult time with two collumn proofs. By which I mean, I am not sure how to tell if I am skipping a step, or which step would come next. Which would affect the other collumn, reasons. If you have any advice on how to successfully solve a proof, it would be gratefully appricieated.
Thank you!
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Writing proofs is a lot different from simply solving a problem because you have to show that a statement holds for all relevant cases. To prevent skipping steps, make sure you ask yourself questions like, "Why is this statement true?" and "How could I use this to further my proof?" You want to be able to back up your statements, e.g. you cannot simply claim that twenty lines intersect at a point (believe me, I had a problem like this before) because the diagram looks like it does. You must also be careful in terms of proving what is asked, e.g. if you want to prove the statement "If it rains, I use an umbrella" you cannot use the statement "If I use an umbrella, it rains" to prove the first one unless you show that the two statements are bijective (one-to-one).
In reality, two column proofs are very rarely used when doing math research; sometimes when writing proofs people will use techniques that a two column proof wouldn't support easily. The sole purpose of a two column proof is to write the steps of a proof sequentially, backing them up.
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