IMOClass 3 › Geometry

Geometry

2D Shapes

2D (flat) shapes can be drawn on paper. A square has 4 equal sides and 4 corners, a rectangle has 4 sides (two long, two short) and 4 corners, a triangle has 3 sides and 3 corners, and a circle is round with no corners.

The straight edges are sides and the points where they meet are corners (vertices).

Example 1: How many sides and corners does a square have?
4 equal sides and 4 corners.
Example 2: How many sides does a triangle have?
3 sides.
Quick recap
  • Square and rectangle: 4 sides, 4 corners.
  • Triangle: 3 sides, 3 corners. Circle: round, no corners.
✓ Quick check
How many corners does a circle have?
A circle is round and has no corners.
How many sides does a rectangle have?
A rectangle has 4 sides.

3D Shapes: Faces, Edges, Vertices

3D (solid) shapes take up space. A cube (like a dice) has 6 faces, 12 edges and 8 vertices. A cuboid (like a brick) also has 6 faces, 12 edges and 8 vertices. A sphere is like a ball, a cylinder like a tin, and a cone like an ice-cream cone.

A face is a flat surface, an edge is where two faces meet, and a vertex is a corner.

Example 1: How many faces does a cube have?
6 faces.
Example 2: A dice is the shape of which solid?
A cube.
Quick recap
  • Cube and cuboid: 6 faces, 12 edges, 8 vertices.
  • Face = flat surface; edge = where faces meet; vertex = corner.
✓ Quick check
How many faces does a cuboid have?
A cuboid has 6 faces.
A ball is the shape of a ___ ?
A ball is a sphere.

Lines & Symmetry

Lines can be straight, curved or slanting. The edge of a ruler is a straight line; the letter S is made of curves.

A shape has line symmetry if a line can divide it into two equal halves that match exactly, like a mirror. That line is called a line of symmetry. A square has 4 lines of symmetry.

Example 1: What kind of line is the edge of a ruler?
A straight line.
Example 2: How many lines of symmetry does a square have?
4 lines of symmetry.
Quick recap
  • Lines can be straight, curved or slanting.
  • A line of symmetry splits a shape into two matching halves.
✓ Quick check
A line that divides a shape into two equal matching halves is called a line of ___ ?
Such a line is called a line of symmetry.
What kind of line is the edge of a ruler?
A ruler's edge is a straight line.
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