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Euclid's first postulate states that 'A straight line may be drawn from any one point to any other point.' Which of these correctly states Euclid's SECOND postulate?

Class 9Introduction to Euclid's GeometryGeometry — Foundations
  • AA line segment can be produced (extended) indefinitely.
  • BA circle can be drawn with any centre and radius.
  • CAll right angles are equal to one another.
  • DThe whole is greater than the part.

Step-by-Step Solution

Postulate 2: a terminated line (segment) can be extended indefinitely. The circle statement is Postulate 3 and all-right-angles is Postulate 4.
Answer: A) A line segment can be produced (extended) indefinitely.

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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