Although there are plenty of kinds of symmetry, elementary school school normally presents just reflective the opposite (or “mirror symmetry”). Together a result, school materials tend come use words symmetry as if it had actually only the one meaning. This post will emphasis on the one meaning, yet illustrate others as well.

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This picture shows a an easy picture with a mirror inserted along the heat of symmetry. The result that one watch — half of the original and also the mirror image of that half — specifically matches the initial figure. Us say that the original figure is “symmetric” v respect come the mirror; it has actually reflective symmetry.

## Reflective symmetry and “line that symmetry”

Mirror-symmetric objects have at least one line the symmetry, a line follow me which the number can be folded right into two precisely matching parts, components that are mirror images of each other.

This figure has two lines that symmetry: the horizontal heat of symmetry cut the figure into a top and also bottom that space mirror photos of every other; the vertical line of symmetry cuts the number into a left and also right that are mirror pictures of every other. The star below has 5 lines of symmetry, five lines on i beg your pardon it deserve to be urgently so the both sides enhance perfectly.

A common misconception uncovered even in countless glossaries and also texts: no all lines that divide a figure into 2 congruent components are currently of symmetry. Because that example, the diagonal line of a (non-square) rectangle is no a line of symmetry.

When a winter is put along the diagonal of a rectangle, the an outcome does not look the very same as the original rectangle, therefore the diagonal is not a line of symmetry. This new shape — the combination of the triangular half of the initial rectangle and its photo in the winter — is dubbed a kite.

## Mirror Play

Well before children begin any formal examine of symmetry, playing v mirrors — maybe on pattern Block designs the they construct — develops experience and also intuition that deserve to serve both their geometric thinking and also their artistic ideas. The colorful design above has just vertical and also horizontal currently of symmetry, however placing a winter on it at an additional angle can produce a beautiful brand-new design.

The an initial figure listed below shows that the letter A has a vertical heat of symmetry, however it’s quite “tame” play. More intrepid experiments give other interesting results.

The very same is true that the letter M.

Letters choose B and D have a horizontal heat of symmetry: your top and bottom components match.

Some letters, because that example, X, H, and O, have actually both vertical and also horizontal present of symmetry.

And some, favor P, R, and N, have no present of symmetry.

## Rotational symmetry

Another the opposite that youngsters sometimes use in your Pattern Block design is “Rotational Symmetry.” A number has rotational the contrary if some rotation (other than a complete 360° turn) to produce the very same figure. For example, this figures, as soon as rotated just the right amount — 360°/3 for the “name” snapshot and 360°/5 for the star — look exactly as castle did before rotation.

The letters, N, Z, and also S likewise share the property.

Note that part figures, like the star and the colorful blob in ~ the height of the page, yet not the letters N, Z, or S, have actually both reflective and rotational symmetry.

## The most symmetric shape

A circle has actually infinitely countless lines of symmetry: any kind of diameter lies ~ above a line of symmetry with the center of the circle. Any type of rotation of any type of amount roughly the center of the circle also leaves the circle unchanged.

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## Books for children

For young children, K-2:Make a enlarge Puddle make a smaller Worm, by Marion WalterFor enlarge children, great 2 and also up:The winter Puzzle Book, by Marion Walter

## What’s in a word?

The “metry” in symmetry and geometry and also metric refers to measurement.