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Euclid wrote that the boundaries of a solid are surfaces, the ends of surfaces are lines (edges) and the ends of lines are points (vertices). For the tent-shaped solid shown (dashed edges are hidden), how many surfaces, edges and vertices are there?

Class 9Introduction to Euclid's GeometryGeometry — Foundations
  • A5 surfaces, 6 edges, 5 vertices
  • B3 surfaces, 9 edges, 6 vertices
  • C6 surfaces, 9 edges, 5 vertices
  • D5 surfaces, 9 edges, 6 vertices

Step-by-Step Solution

Surfaces: 2 triangles + 3 rectangles . Edges: 6 solid + 3 hidden . Vertices: 3 at the front + 3 at the back . Check: .
Answer: D) 5 surfaces, 9 edges, 6 vertices

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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