I'm in 9th grade accelerated geometry(honors class.) We have been doing 2 column proofs and I just don't understand them. It started simply enough with addition, subtraction, transitive, etc. Now there is the linear pair postulate, vertical angles, corresponding angles, alternating interior/exterior, SSS,AAS,SAS ASA....I just don't know how to prove the answers, and it is really frustrating. Every time I think I understand it, I get confused again. Does anybody have any suggestions on how to know what steps solve what proofs?
2006-11-06 10:47:17 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The best way to attack proving problems in geometry is to answer and answer more proving related problem. No one can help to solve a problem. No one can help you speed up how you solve. It's you who can do that.
Most of my classmates want to be good in algebra.
But they hate to solve algebraic proble,.
I told them to try answering all the questions and exercises in a book of algebra. At first, they did not believe what I have told them. Until they realize that they are becoming better and better in attacking problems in algebra.
So i think, it's up tp you if you will be good in proving geometric relations.
I have also done it myself.
And i can't believe believe that i can answer a problem with ease. It only took me a few second to answer a problem that my classmates took lots of minutes to answer.
Believe me. Solve and solve lots of problem. And you will soon realize that you will solve difficult problems with ease.
2006-11-06 11:04:36 · answer #1 · answered by bhen 3 · 0⤊ 1⤋
OK. This is a broad topic, but my guess is that you struggled with algebra.
Basically, the goal is to start with something that you know and work towards what you would like to show. The rest of mathematics from here on will involve proofs, so you might as well get to like it.
One trick that I occasionally use is to start at the result ("To Prove" or "Show That") and to try work backwards from there to the assumptions ("Given"). When this works, you just present the proof as if you had discovered it in the proper order. No one will know the difference.
Another technique is to start listing all of the implications of the assumptions and why you know them to be true. For isntance, if two angles form a linear pair, the sum of their measures must be 180 degrees. What else do I know? Two angles are congruent, so their measures are equal. OK So, if two congruent angles form a linear pair, they must each be half of 180 degrees or 90 degrees and hence right angles. That was the first proof that I did in Geometry back when I was your age and I still remember it very well. Easy? Of course!
One or two of those implications may look like a step in the right direction of the result. Basically, when you have a drawing, it is often helpful to mark off things that you discover to be congruent as you go. Maybe that fact will have other helpful implications.
Some proofs are one liners. (I really like the proof in abstract algebra that left identity "e" and right identity "f" are actually the same: "e=ef=f" That's the shortest proof that I know!) The proof of Fermat's Last Theorem took over 100 pages and almost 400 years to discover. It ended up being morphed into a couple of equivalent problems before someone actually solved it! Be thankful that you don't have to try to prove Fermat!
Mathematics isn't about memorization. It's about insight and discovery. Geometry is the first chance that you have to experience that. Enjoy yourself. It's your first opportunity to think up answers for yourself and be able to prove that you are right. What a concept!
2006-11-06 19:28:25 · answer #2 · answered by Mich Ravera 3 · 3⤊ 0⤋
At each step there are a limited number of possible steps. First try to see them all. Then try ruling out possibilities.
2006-11-09 16:38:36 · answer #3 · answered by Aaron A 3 · 0⤊ 0⤋