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In connection with proof in geometry , indicates which one of the following statement is incorrect:
A. Some statements are accepted without being proved.
B. In some instances there is one more than one correct order in proving certain propositions.
C. Every term used in a proof must have been defined previously.
D.I t is not possible to arrive by correct reasoning as a true conclusion if, in the given, then is an untrue proposition.
E. Indirect proof can be used whenever there are two or more contrary propositions.

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Last updated date: 24th Jul 2024
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Answer
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Hint: In this question we have to consider each statement and check if it’s true or not. A geometry proof -like any mathematical proof is an argument that begins with known fact, proceeds from there through a series of logical deductions, and ends with things you are trying to prove.

Complete step-by-step answer:
There are three types of proof in geometry: first is Direct proof (proof by construction) second is Proof by contradiction and third Proof by induction.
Statement A is correct because a statement is always true and doesn’t need proof, it is axiom …….A statement that has been proven by logical arguments based on axiom, is a theorem.
Statement B is incorrect because in some instances there is more than one correct order in proving a certain proposition is incorrect because there is only one correct order in proving certain propositions.
Statement C is correct because a mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumption logically guarantees the conclusion. The argument may use other previously established statements.
 Statement D is correct because if a valid argument does have a false conclusion, it cannot have all true premises. Thus at least one premise must be false, then the conclusion must be false.
In this statement E indirect proof can be used whenever there are two or more country propositions that are correct. A contradictory statement is one that says two that cannot be true.
So after checking all the statements we find that statement B is incorrect.

So, the correct answer is “Option B”.

Note: Read all the given statements carefully and find the reason for their true or false it helps you to find your answers easily. Always look for the right statement first.