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Which one of these is an AXIOM (common notion)?

Class 9Introduction to Euclid's GeometryGeometry — Foundations
  • AA circle can be drawn with any centre and any radius.
  • BAll right angles are equal.
  • CThings equal to the same thing are equal to each other.
  • DA straight line can be drawn between any two points.

Step-by-Step Solution

Universal truth (used in arithmetic, algebra, geometry) → AXIOM. The other three are specific geometry assumptions → POSTULATES.
Answer: C) Things equal to the same thing are equal to each other.

Key idea: The five postulates of Euclid

**Postulate 1**: A straight line may be drawn from any one point to any other point.

**Postulate 2**: A terminated line (segment) can be produced indefinitely (extended).

**Postulate 3**: A circle can be drawn with any centre and any radius.

**Postulate 4**: All right angles are equal to one another.

**Postulate 5** (the famous one): If a straight line falling on two straight lines makes the interior angles on the same side together less than two right angles (180°), then the two lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.

These 5 statements are the seeds. Everything else in classical geometry grows from them.

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