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.
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.