What is Symmetry in Math

Definition of Symmetry

Symmetry is when a shape looks identical to its original shape after being flipped or turned. Symmetry is thus a mirror image. Symmetry exists everywhere in our life. Symmetry exists in patterns.

What is a Line of Symmetry?

The line of symmetry or Reflection symmetry divides the shape into two identical parts. The line can be vertical, horizontal or diagonal. Peter Weatherhall’s song is a mnemonic that helps us remember it.
“Take a shape
And you can see if there is a line of symmetry
When you try folding it
Matching halves are going to fit.”

If we look at ourselves, we have two matching hands, feet, eyes, ears, our smile etc. Our nose can also be divided into two symmetrical parts. But if we take the side view of our face and fold it, we do not get symmetrical shapes as one part is the head and one part is the face.

If we take a plane or a butterfly or a building and fold it, we have symmetrical shapes.

Point Symmetry

When a shape is rotated 180° it looks the same or it looks same when turned upside down. If we take playing cards we see they have point symmetry as they are similar from bottom and top; and even if cut diagonally.

Examples from our Alphabets

The letters A, M and U has vertical symmetry while B and K have horizontal symmetry. S and Z have point symmetry. But the letters F, G, P and R have no symmetry.

Examples from Real Life

If you look closely at bees’ honeycombs, you will see hexagonal symmetry with each circle allowing for maximum storage of honey.

Why does the enormous sun and tiny moon look the same size during a solar eclipse? The sun is 400 times larger than the moon and 400 times further away than the moon too; so by symmetry they look the same size.

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