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Aesthetic_Mess's avatar

Can you help me with proofs?

Asked by Aesthetic_Mess (7887points) October 14th, 2010

I’ve been trying to do proofs in Geometry, and I’m really bad at them. After I write in the ‘Statements’ column the Given, and then in the ‘Reasons’ column that it is the Given, I have no idea where to go from there. It’s pretty sad I know, but can you help me figure out how to do it?

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4 Answers

roundsquare's avatar

Are you able to do stuff without the two column style? By that, I mean are you able to “see” why whatever you are trying to prove is true? Could you explain it in and pictures, etc…?

lapilofu's avatar

There’s no bulletproof tactic for writing a proof—if there were, we wouldn’t need so many mathematicians at universities. Write another statement that follows logically from the Given and explain why it follows. Then write another that follows from that. See if you get any closer to what you’re trying to prove. Be prepared to cross things out and try different approaches.

The more proofs you write, the more you will improve your sense of what will get you closer to the proposition you’re trying to prove. Until then you have to experiment a little.

LostInParadise's avatar

It sometimes helps to work your way backwards from the conclusion. For example, if you need to show that two triangles are congruent, you might ask what additional corresponding parts of the triangles might you be able to show are congruent. Then think of how to work forward to show those parts are congruent.

MissPoovey's avatar

My trick was always to try to disprove first. Think of ways that show its false. Kind of like arguing back against yourself.
That will eliminate the dead ends and will point you in the right direction.
But like @lapilofu says, the more you write, the better you get.

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