Bilateral Symmetry - Geometry Made Easy
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# Bilateral Symmetry

Thanks to Wikimedia Commons

A shape has bilateral symmetry when it is the same on both sides of a line drawn down the middle. You are (mostly) bilaterally symmetrical, because if I drew a line down through your nose perpendicular to the ground, you'd have one eye, one arm, and one leg on each side of the line. This butterfly has bilateral symmetry too, with one wing and one antenna on each side of the red line.

Some geometric shapes have bilateral symmetry, while others don't. For example, a square has bilateral symmetry, and so does a circle, and so does a rectangle. An isoceles triangle has bilateral symmetry. But most parallelograms do not have bilateral symmetry. A rhombus does not have bilateral symmetry vertically, but it does if you draw a diagonal line connecting two opposite corners (thanks to Jeffrey Paules for pointing this out!).

Three-dimensional solids can have bilateral symmetry, too. A sphere and a cube both have bilateral symmetry.

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Karen Carr is Associate Professor Emerita, Department of History, Portland State University. She holds a doctorate in Classical Art and Archaeology from the University of Michigan. Follow her on Instagram, Pinterest, or Twitter, or buy her book, Vandals to Visigoths.
Karen Carr is Associate Professor Emerita, Department of History, Portland State University. She holds a doctorate in Classical Art and Archaeology from the University of Michigan. Follow her on Instagram or Twitter, or buy her book, Vandals to Visigoths.
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