Basics of symmetry

Basics of symmetry

In this lesson, we will learn:

  • How to identify symmetrical vs. asymmetrical shapes or pictures
  • How to check symmetry lines with the folding method or mirror test method

Notes:

  • A "symmetrical" shape is made up of exact same parts facing each other
    • A line of symmetry divides a symmetrical shape into 2 congruent parts
    • If the shape is not symmetrical it is "asymmetrical"
Basics of Symmetry
  • Check if a shape has a line of symmetry by folding it in half to see if the parts match up
Basics of Symmetry
    • or using a mirror test: laying the picture/shape flat and putting a mirror on a possible symmetry line to see if the mirrored image matches with the original
Basics of Symmetry
  • Some shapes have more than one line of symmetry. Regular polygons have the same number of symmetry lines as number of sides

  • Ex. triangles = 3 sides = 3 symmetry lines Basics of Symmetry
    • some words (alphabet letters) and numbers also have symmetry:

Basics of Symmetry

Lessons

  • Introduction
    Introduction to Basics of Symmetry:
    a)
    What is symmetry? What is a symmetrical shape?

    b)
    Folding test for lines of symmetry

    c)
    Mirror test for lines of symmetry

    d)
    Symmetry in alphabet letters and numbers


  • 1.
    Congruent parts and lines of symmetry
    A dotted line breaks the shape into two parts.
    • Is it a line of symmetry?
    • Are the parts congruent?
    a)
    Basics of Symmetry

    b)
    Basics of Symmetry

    c)
    Basics of Symmetry

    d)
    Basics of Symmetry


  • 2.
    Line of symmetry
    Draw a line of symmetry for the shape.
    a)
    Basics of Symmetry

    b)
    Basics of Symmetry

    c)
    Basics of Symmetry

    d)
    Basics of Symmetry

    e)
    Basics of Symmetry

    f)
    Basics of Symmetry


  • 3.
    Multiple lines of symmetry
    Draw two possible lines of symmetry.
    a)
    Basics of Symmetry

    b)
    Basics of Symmetry

    c)
    Basics of Symmetry


  • 4.
    Symmetrical shapes on a dot grid
    Using the dot grid, finish drawing the shape. The line of symmetry and half of the shape are shown.
    a)
    Basics of Symmetry

    b)
    Basics of Symmetry

    c)
    Basics of Symmetry


  • 5.
    Symmetry of regular polygons
    a)
    For each regular polygon, draw all possible lines of symmetry and fill out your answers in the table.
    Basics of Symmetry

    b)
    Following the pattern for regular polygons, how many lines of symmetry would a heptagon have?

    c)
    Following the pattern for regular polygons, how many lines of symmetry would an octagon have?