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Symmetry has been an important aspect of human design for millennia. In fact, the symmetry in manmade objects often outstrips the level of symmetry present in the natural world. So which is more beautiful, a perfectly symmetrical building or a nearly-perfect snowflake? Can total asymmetry be just as beautiful?

In this lesson students analyze the symmetry of objects and use geometric reflections to construct symmetrical images of their own. They will then use ideas of symmetry and asymmetry to debate the nature of beauty and perfection.

Students will

  • Analyze objects for their symmetry and draw lines of symmetry
  • Reflect an object across a line of symmetry using a coordinate plane to match corresponding points of the original and reflected image
  • Analyze natural objects and their manmade equivalents to determine which type of object is more perfectly symmetrical
  • Debate the merits of symmetry, near symmetry, and asymmetry and the ways in which each can be seen as beautiful

Before you begin

Students may benefit from some initial exposure to symmetry, but this lesson can also be used to introduce the concept.

Common Core Standards

Content Standards
Mathematical Practices


BBC, Dove. Photo credit: Mohammad Reza Domiri Ganji