Postulates, definitions, conjectures, and theorems each have distinguishing features that help identify them. Which of the following answer choices accurately represents the term’s distinguishing feature? (1 point) Responses A theorem is assumed to be true, and it does not have to be proven. A theorem is assumed to be true, and it does not have to be proven. A postulate is assumed to be true, and it does not have to be proven. A postulate is assumed to be true, and it does not have to be proven. A conjecture tells you what a term means or what to do with a concept. A conjecture tells you what a term means or what to do with a concept. A definition is a statement that is made based on observations that must be proven true. A definition is a statement that is made based on observations that must be proven true.

Answer 1

The correct distinguishing feature among the choices provided is: A postulate is assumed to be true, and it does not have to be proven.

To clarify:

• Postulates (or axioms) are statements accepted as true without proof and serve as the foundational building blocks for further reasoning in mathematics and logic.
• Theorems are statements that have been proven to be true based on postulates, definitions, and previously established theorems.
• Definitions provide precise meanings for terms and concepts but do not intrinsically hold truth or require proof.
• Conjectures are propositions that are suspected to be true based on observations but have not yet been proven or disproven.

Given these distinctions, the response “A postulate is assumed to be true, and it does not have to be proven” is accurate.