I understand for the most part what proofs are, but I think I'm missing something because I keep getting them wrong.
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You need to try to identify and make a clear difference between what information is given by the problem and what conclusion you need to prove.
When you need to solve a geometry problem, if the problem does not provide the request of the problem along with a corresponding draw, try to sketch yourself a draw that helps you to visualize what it is given and what is it requested.
The statements you will make will be based on the conclusion you need to prove. The postulates and theorems need to support you statements.
Try to collect all information listed above in a two column proof that helps you to split all statements in steps that make easy your deductive reasoning.
Proofs can be very difficult. I am assuming you are meaning two column proofs in Geometry class.
In short, one step of each argument has to be supported by some rule, theorem, postulate, etc. There isn't necessarily any one correct answer, for there can be a lot of ways to do these geometry proofs. That's one reason why I tried to work with my students when the textbooks have a two column proof for the students to do, half of it filled in. The textbook was already looking for it to be done one specific way, which can be harder to consider.
In short, for proofs, it a lot like any other math problem, except you know the answer; you just need to show how to solve the problem. So, for instance, if we had:
x+5 = 9
We know the answer is x = 4, but why? Because you would subtract 4 from each side:
x+5 = 9
x = 4
But, what says we can subtract 5 from each side? Why can we do that? It's because of the subtraction property of equality:
x+5 = 9 Given
Subtract 5 from each side Subtraction property of equality
x = 4 Answer
I hope this helps.
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