Shapes and Symmetry | Year 8 Mathematics (Cambridge) PDF Download

Shapes and Symmetry

Properties of 2D Shapes

• Triangles: Triangles have three sides and three angles. Examples include equilateral, isosceles, and scalene triangles.
• Quadrilaterals: Four-sided shapes with different properties like squares, rectangles, parallelograms, and rhombuses.
• Polygons: Shapes with many sides, such as pentagons, hexagons, and octagons.

Lines of Symmetry

• A line that divides a shape into two equal halves that mirror each other.
• Examples:
  • A square has 4 lines of symmetry.
  • An equilateral triangle has 3 lines of symmetry.
  • A circle has infinite lines of symmetry.

Rotational Symmetry

• When a shape can be rotated by less than a full circle (360 degrees) and still look the same.
• Examples:
  • A square has rotational symmetry of order 4 (90 degrees).
  • An equilateral triangle has rotational symmetry of order 3 (120 degrees).
  • A circle has rotational symmetry of infinite order (any angle).

Examples of Shapes and Symmetry

• Example 1: Properties of a Square
  • A square has four equal sides and four right angles.
  • It has both rotational symmetry (order 4) and four lines of symmetry.
• Example 2: Lines of Symmetry in a Rectangle
  • A rectangle has two lines of symmetry—one horizontally through the middle and one vertically through the middle.
• Example 3: Rotational Symmetry in an Equilateral Triangle
  • An equilateral triangle can be rotated by 120 degrees and still look the same, demonstrating rotational symmetry of order 3.

Practical Applications

Understanding shapes and symmetry helps in:

• Architecture and design.
• Art and patterns.
• Identifying shapes in everyday objects.

Summary

Shapes have different properties like sides and angles. Symmetry includes lines that divide shapes equally and rotational symmetry where shapes look the same after rotation. Understanding these concepts helps in various practical applications and creative fields.