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In each panel, Rohan joins every pair of marked points with a straight line (extended both ways). How many different lines does he get in panels (i), (ii) and (iii) respectively?

Class 9Introduction to Euclid's GeometryGeometry — Foundations
  • A1, 3 and 3
  • B2, 3 and 3
  • C1, 1 and 3
  • D1, 2 and 3

Step-by-Step Solution

Exactly one line passes through two distinct points. In (ii) P, Q, R lie on one straight line (collinear), so all pairs give the same line. In (iii) X, Y, Z are not collinear, so the 3 pairs give 3 different lines.
Answer: C) 1, 1 and 3

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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