We see shapes and patterns everywhere! In this chapter we identify 2D shapes, explore their properties, and study tessellations, symmetry, and repeating patterns.
Key Concepts
- 2D Shapes and Properties:
- Triangle: 3 sides, 3 angles, 3 vertices
- Quadrilateral: 4 sides, 4 angles (includes square, rectangle, rhombus, parallelogram, trapezium)
- Circle: No straight sides, no angles, 1 curved boundary
- Pentagon: 5 sides; Hexagon: 6 sides; Octagon: 8 sides
Symmetry: A shape has line symmetry if one half is a mirror image of the other. The dividing line is called the line of symmetry (or axis of symmetry).
Tessellation: A pattern of shapes that fit together without any gaps or overlaps. Triangles, squares, and regular hexagons tessellate perfectly.
Tiling Patterns: Repeating arrangements of one or more shapes to cover a surface.
- Perimeter of common shapes:
- Square: 4 x side
- Rectangle: 2 x (l + w)
---
How many lines of symmetry does a square have?
- A square has 4 lines of symmetry: 2 along the diagonals and 2 through the midpoints of opposite sides.
---
Name a shape that tessellates.
- A regular hexagon tessellates (honeycomb pattern).
---
How many sides does a hexagon have?
- A hexagon has 6 sides.
---
Does a circle have a line of symmetry?
- Yes, a circle has infinite lines of symmetry (any diameter is a line of symmetry).
---
What is the next shape in the pattern: triangle, square, pentagon, hexagon, ___?
- Each shape has one more side than the previous. Hexagon has 6 sides, so next is heptagon (7 sides).
---
Key Facts
- Equilateral triangle: 3 lines of symmetry
- Rectangle: 2 lines of symmetry
- Square: 4 lines of symmetry
- Regular hexagon: 6 lines of symmetry
Common mistakes
- Thinking a rectangle has 4 lines of symmetry like a square. A rectangle only has 2 (not along diagonals).
- Confusing the number of sides of hexagon and heptagon.
Summary
Shapes are classified by the number of sides and angles. Symmetry means one half mirrors the other. Tessellations cover a surface without gaps or overlaps.