Final answer:
A postulate is a fundamental assumption in geometry used as a starting point for further reasoning, while a common notion is a statement that is widely accepted without proof. The correct matching will align postulate with the definition of a fundamental assumption and common notion with a statement accepted without proof.
Step-by-step explanation:
By defining terms such as postulate and common notion, we can better understand the language of geometry, which is pivotal in mathematical reasoning.
A postulate is a fundamental assumption that serves as the basis for reasoning, often used to construct the rest of a geometric theory. On the other hand, a common notion is understood to be a statement accepted without proof, which generally addresses the innate understanding or reasoning accepted by all without debate.
In the context of the question, the correct matches would be:
- Postulate: a) A fundamental assumption that serves as the basis for reasoning.
- Common Notion: b) A statement accepted without proof.