Math - 2018-19

2.12 - Symmetry

The student will

a) draw a line of symmetry in a figure; and

b) identify and create figures with at least one line of symmetry

Adopted: 2016


So that I can recognize balance and symmetry in art and nature

So that I can understand that symmetry results in two equal parts of an object, animal, building, or picture


  • A line of symmetry divides a figure into two congruent parts each of which is the mirror image of the other.  An example is shown below:

    Lines of symmetry are not limited to horizontal and vertical lines.
  • Children learn about symmetry through hands-on experiences with geometric figures and the creation of geometric pictures and patterns.
  • Guided explorations of the study of symmetry using mirrors, paper folding, and pattern blocks will enhance students’ understanding of the attributes of symmetrical figures.
  • Congruent figures have exactly the same size and shape.  Noncongruent figures do not have exactly the same size and shape.  Congruent figures remain congruent even if they are in different spatial orientations. 
  • While investigating symmetry, children move figures, such as pattern blocks, intuitively, thereby exploring transformations of those figures. A transformation is the movement of a figure—either a translation, rotation, or reflection. A translation is the result of sliding a figure in any direction; rotation is the result of turning a figure around a point or a vertex; and reflection is the result of flipping a figure over a line. Children at this level do not need to know the terms related to transformations of figures.


The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

  • Draw a line of symmetry in a figure (a)
  • Identify figures with at least one line of symmetry, using various concrete materials (e.g., mirrors, paper folding, pattern blocks) (b)
  • Determine a line of symmetry that results in two figures that have the same size and shape and explain reasoning (a, b)
  • Create figures with at least one line of symmetry using various concrete materials (b)


Updated: Aug 22, 2018