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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.
so that they can have a clear an valid point to the argument, with proof.
It is possible to draw a straight line from any point to any other point.
A statement that is subjective, ambiguous, or based on opinion cannot be used to explain the steps of a proof. In a mathematical proof, each step must be based on objective facts, definitions, axioms, or previously proven theorems in order to ensure the validity and rigor of the argument. Statements that rely on personal beliefs, feelings, or interpretations are not suitable for constructing a logical proof.
A vertex is a point where two or more lines meet.