Question 627286: Is it possible that two different reasons can justify a step in a proof? Why or why not? Is it easier to work down the columns or across the rows in a proof? Why? Make sure you justify your opinion.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Of course it is possible. It depends on the nature of the statement you want to justify. One possible situation would be where you are given a piece of information that is just as easily justified by a definition, axiom, or theorem. For example, say that you were asked to prove that the two triangles formed by creating the altitude to the apex of an isosceles triangle are congruent, but not only were you told that the triangle is isosceles, but you were also given that the two base angles were of equal measure. In this situation you can state that the two base angles are equal in measure (as part of setting up your SAS proof of congruency) because it is a given fact or because of the definition of isosceles.
I'm not sure what you mean by "working down the columns" vs. "working across the rows", unless you are saying "is it better to write down all of the statements that you intend to use first and then go back and fill in the reasons or is it better to put the reason down for each statement step as you go?" I'm not sure that an absolute statement can be made one way or the other. Sometimes I work both ends against the middle, going as far as I can from the top and then working backwards from what I want to prove. Strategizing proofs is as much an art as a science. Disabuse yourself of the notion that there is some magical process that will work for every proof you are ever going to encounter. The only thing that works consistently is practice, practice, and more practice.
John
My calculator said it, I believe it, that settles it
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