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Which is the correct distinction between an axiom and a postulate as taught in this chapter?

Class 9Introduction to Euclid's GeometryGeometry — Foundations
  • AAn axiom is a universal truth; a postulate is a geometry-specific assumption.
  • BAn axiom is geometry-specific; a postulate is universal.
  • CBoth must be proved before use.
  • DAn axiom is proved; a postulate is assumed.

Step-by-Step Solution

Axioms apply across all of mathematics; postulates are starting assumptions specific to geometry. Both are accepted without proof.
Answer: A) An axiom is a universal truth; a postulate is a geometry-specific assumption.

Key idea: Axiom vs Postulate — the difference

Both are starting assumptions, accepted without proof. The difference is **scope**:

- **Axiom**: a universal truth used across all of mathematics (arithmetic, algebra, geometry).
- **Postulate**: a starting assumption specific to one subject — for Euclid, geometry.

Modern mathematicians often blur this distinction and use 'axiom' for both, but at this level you must keep them separate.

Example:
- 'If equals are added to equals, the wholes are equal' → AXIOM (general arithmetic).
- 'A circle can be drawn with any centre and radius' → POSTULATE (only about geometry).

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