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What is Symmetric Shapes, Figures and Patterns

What is Symmetry?

Symmetry in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, “symmetry” has a more precise definition, that an object is invariant to any of various transformations; including reflectionrotation or scaling. Although these two meanings of “symmetry” can sometimes be told apart, they are related, so they are here discussed together. The opposite of symmetric shapes is asymmetric shapes.

symmetric shapes

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What is Symmetric Shapes In Geometry

A geometric shape or object is symmetric if it can be divided into two or more identical pieces that are arranged in an organized fashion. This means that an object is symmetric if there is a transformation that moves individual pieces of the object but doesn’t change the overall shape.

  • An object has reflectional symmetry, if there is a line going through it which divides it into two pieces which are mirror images of each other.
  • An object has rotational symmetry if the object can be rotated about a fixed point without changing the overall shape.
  • An object has translational symmetry if it can be translated without changing its overall shape.
  • An object has helical symmetry if it can be simultaneously translated and rotated in three-dimensional space along a line known as a screw axis.

Symmetric Shapes

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What is a Symmetric Shape?

If a figure/shape can be folded or divided into half so that the two halves match exactly then such a figure/shape is called a symmetric shape.

The shapes below are all symmetric shapes.

symmetric shapes

The dotted line in each of the symmetric figures above that divides the figure into two equal halves is called the line of symmetry.

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  • Folding Test

I have folded a rectangle one way, and it didn’t work.

symmetric shapes

So this is not a Line of Symmetry.

When I try it this way, It does work (the folded part sits perfectly on top, all edges matching):

symmetric shapes

So this is a Line of Symmetry.


  • Triangle Test

A Triangle can have 3, 1 or no line of symmetry. Therefore triangle is also included in symmetric shapes.

symmteric shapes

    • Circle Test

A line that goes through circle’s center is a Line of Symmetry. So a Circle has infinite Lines of Symmetry.

symmetric shapes

How to Make Symmetric Shapes

  • Step 1: Take a piece of paper and fold it.

symmetric shapes

  • Step 2: Cut out any figure which starts and ends on the fold line such as the one shown below.

symmetric shapes


  • Step 3: Unfold the figure. You have a symmetric figure where the fold line is the line of symmetry.

symmetric shapes

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Updated: October 16, 2017 — 4:20 pm

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