2D Shapes Chapter Notes | Year 6 Mathematics IGCSE (Cambridge) PDF Download

Quadrilaterals

• The objective is to identify quadrilaterals.
• Describe quadrilaterals.
• Classify quadrilaterals.
• Sketch quadrilaterals.
• Quadrilaterals:
  • Four-sided polygons used in applications like tiling kitchens and bathrooms due to their ability to tessellate (fit together without gaps).
  • Types include square, rectangle, parallelogram, trapezium, isosceles trapezium, rhombus, and kite.
• Properties of quadrilaterals:
  • Square:
    • Four equal sides.
    • Two pairs of parallel sides.
    • All angles are 90°.
    • Diagonals bisect each other at 90°.
    • Four lines of symmetry (horizontal, vertical, two diagonals).
  • Rectangle:
    • Two pairs of equal sides.
    • Two pairs of parallel sides.
    • All angles are 90°.
    • Diagonals bisect each other.
    • Two lines of symmetry (horizontal and vertical).
  • Parallelogram:
    • Two pairs of equal sides.
    • Two pairs of parallel sides.
    • Two pairs of equal angles.
    • Diagonals bisect each other.
    • No lines of symmetry (unless it is a rectangle or square).
  • Trapezium:
    • One pair of parallel sides.
    • Other properties vary depending on the specific trapezium.
  • Isosceles Trapezium:
    • One pair of parallel sides.
    • One pair of equal sides (non-parallel sides).
    • One pair of equal angles (at the base or top).
    • One line of symmetry.
  • Rhombus:
    • Four equal sides.
    • Two pairs of parallel sides.
    • Two pairs of equal angles.
    • Diagonals bisect each other at 90°.
    • Two lines of symmetry (along diagonals).
  • Kite:
    • One pair of equal sides (adjacent sides).
    • Diagonals meet at 90°.
    • One line of symmetry (through the diagonal connecting the equal angles).
• Tessellation:
  • Some quadrilaterals (e.g., squares, rectangles, parallelograms, rhombuses) tessellate, fitting together without gaps.
  • Not all quadrilaterals tessellate (e.g., some kites and trapezia may not).
• Decomposing quadrilaterals:
  • Break into simpler shapes, e.g., a square can be decomposed into two triangles, two trapezia, or a rectangle and two triangles.
• Applications include graphic design (packaging shapes) and architecture (tiling patterns).

Circles

• The objective is to learn the names of the parts of a circle.
• Draw circles accurately.
• Parts of a circle:
  • Centre: The fixed point equidistant from all points on the circle.
  • Radius: The distance from the centre to any point on the circle.
  • Diameter: A line through the centre joining two points on the circumference, equal to twice the radius (diameter = 2 × radius).
  • Circumference: The perimeter of the circle, the distance around it.
• Drawing circles:
  • Use compasses set to the radius length, e.g., for a radius of 4 cm, open compasses to 4 cm, place the point at the centre, and rotate to draw the circle.
  • Label the centre, radius, diameter, and circumference.
  • Example: A circle with radius 3 cm has diameter 6 cm (2 × 3 = 6); a circle with diameter 60 mm has radius 30 mm (60 ÷ 2 = 30).
• Relationship between radius and diameter:
  • diameter = 2 × radius or radius = diameter ÷ 2.
  • Example: Circles with radius = 2 cm or diameter = 4 cm are the same size.
• Applications include drawing precise circular shapes in design or geometry problems.

Rotational symmetry

• The objective is to identify shapes and patterns with rotational symmetry.
• Describe rotational symmetry.
• Rotational symmetry:
  • A shape has rotational symmetry if it looks the same after being rotated about a central point by a certain angle before completing a full turn.
  • The order of rotational symmetry is the number of times the shape looks identical during one full 360° rotation.
• Examples:
  • Rectangle: Order 2 (looks the same after 180° and 360° rotations).
  • Parallelogram: Order 2 (looks the same after 180° and 360°).
  • Isosceles trapezium: Order 1 (only looks the same after a full 360° turn).
  • Equilateral triangle: Order 3 (looks the same after 120°, 240°, and 360°).
  • Scalene triangle: Order 1 (no rotational symmetry except full turn).
  • Square: Order 4 (looks the same after 90°, 180°, 270°, and 360°).
• Patterns and combined shapes:
  • Rotational symmetry of patterns depends on how shapes are joined, e.g., joining two tiles may change the order of rotational symmetry based on the resulting pattern.
  • Example: A button with a four-pointed star has order 4.
• Relationship with line symmetry:
  • Some shapes have the same number of lines of symmetry as their order of rotational symmetry (e.g., square: 4 lines, order 4), but this is not always true (e.g., parallelogram: 0 lines, order 2).
  • Shapes with no line symmetry may still have rotational symmetry (e.g., parallelogram), but those with order 1 often lack line symmetry (e.g., scalene triangle).
• Applications include designing objects like road signs, buttons, or playground equipment (e.g., roundabouts) that rely on rotational symmetry for aesthetic or functional purposes.