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Which statement is a POSTULATE (geometry-specific)?

Class 9Introduction to Euclid's GeometryGeometry — Foundations
  • AIf equals are added to equals, the wholes are equal.
  • BThe whole is greater than the part.
  • CA terminated line can be produced indefinitely.
  • DThings which are halves of the same things are equal.

Step-by-Step Solution

Specific to geometry (about lines) → postulate (Euclid's 2nd). The others are general axioms.
Answer: C) A terminated line can be produced indefinitely.

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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