A true statement that can be proven is that the sum of the interior angles of a triangle is always 180 degrees. This can be demonstrated through various methods, such as using parallel lines and transversals or by employing geometric proofs. Regardless of the type of triangle—whether it is scalene, isosceles, or equilateral—this rule holds true universally in Euclidean geometry.
True
A statement which appears to be true but has not been proven to be so, is a postulate.
A conjecture is an unproven statement or hypothesis that is proposed based on observations or patterns. When a conjecture is proven true through logical reasoning or mathematical proof, it becomes a theorem. For example, the conjecture that "the sum of the angles in a triangle is always 180 degrees" is a statement that can be proven true in Euclidean geometry.
Neither. A theorem is a proven mathematical statement. This says nothing about how easily it can be proven. e.g. the Pythagorean Theorem is easily proven, but Fermat's Last Theorem is extremely difficult to prove.
It must be proven to be true by several different individuals not known to each other.
False. It is proven to be true IF some axioms are assumed to be true. A mathematical statement can be proven to be true only after some axioms have been assumed.
theorem
True
An objective statement is based on facts and can be proven true or false, while a subjective statement is based on personal opinions or feelings and cannot be proven true or false.
A statement that can be proven true or false. Not a question, not a command, and not an opinion.
A statement which appears to be true but has not been proven to be so, is a postulate.
Theorem
A claim is a statement that asserts something to be true, but may not necessarily be proven. A fact, on the other hand, is a statement that is proven to be true through evidence or data.
Such a statement is called a theorem.true
Every statement apart from the axioms or postulates.
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theorem