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How do you do proofs?
A proof is a very abstract thing. You can write a formal proof or an informal proof. An example of a formal proof is a paragraph proof. In a paragraph proof you use a lot of deductive reasoning. So in a paragraph you would explain why something can be done using postulates, theorems, definitions and properties. An example of an informal proof is a two-column proof. In a two-column proof you have two columns. One is labeled Statements and the other is labeled Reasons. On the statements side you write the steps you would use to prove or solve the problem and on the "reasons" side you explain your statement with a theorem, definition, postulate or property. Proofs are very difficult. You may want to consult a math teacher for help.
which completes the paragraph proof of the congruent supplement theorem?
A+
What does justify mean in math terms?
In math terms, it is more or less to make something sound reasonable; but in a way that is less formal than a proof.
Second type of proof in geometry is a proof by?
I am not really sure what you are asking but there are 3 types of proofs in geometry a flow proof, a 2-collumn proof, and a paragraph proof.
What about proof by pictures in math?
They are usually not valid.
