How to Do Math Proofs
Proofs are math problems first encountered in geometry. The object of a proof is to show the steps that prove a theorem, written as a list of math statements. Sometimes words are added to explain if the statement is a given, or can be concluded from a given based on a proven theorem. The steps for solving a math proof are listed below.
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Instructions
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Understand the math problem or theorem. Be sure you know what elements are givens, and what you want to prove.
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List the givens, or statements that you accept as true as you write the proof. Anything that's described in the problem may be applicable, so leave nothing out. If something is a given, but isn't in math terms, translate it to a math statement.
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Develop a mental plan of how to get from the first assumption, a basic given, to the theorem that you want to prove. Ask yourself if each step is correct, or if it could be wrong, and why. Write it down if that helps.
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Write a first step. This step is the first given, an assumption that helps you reach the conclusion, which is the statement you want to prove. Follow it with a conclusion that comes logically from that assumption. Write these steps as mathematical formulas.
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Make your math proof step-by-step, and in order. Each step should flow logically from the previous step. Build every step on all the steps that came before it. If a step is an assumption, follow it with a conclusion that leads to the next assumption.
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Ask for help from your math teacher or classmates if you need it to complete the proof. Asking questions is part of learning.
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Conclude the proof with the theorem that you've been proving. The theorem should be the only logical conclusion from your steps.
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Think about your proof. What you should have learned is not the answer to the problem, but how to reach a logical conclusion. Before you turn in the proof, make certain that all steps are either assumptions or conclusions; if any aren't, remove them.
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Tips & Warnings
Look at other completed proofs that are similar to your problem. They can help you learn how to do proofs, and may help you write the steps for your proof.
Sometimes it's easier to figure out your steps if you start with the theorem and work backwards to a given. You'll then write it from the given to the theorem.
There's no single correct answer to a proof; your steps may be different from your classmate's, but if they both prove the theorem, they're both correct.
Don't leave out any step, even if you think it should be obvious.
