Common Core Math Vocabulary

Symmetry - Definition with Examples

What is Symmetry?

Look at these two images of butterflies. What difference do you see?

Symmetry

The first butterfly looks exactly the same from both the left and right sides while the second butterfly does not look the same from the left and right sides.

The images which can be divided into identical halves are called symmetrical. The images that cannot be divided into identical halves are asymmetrical.

 

You must have seen the following symmetrical objects in your surroundings:

Symmetrical objects

 

Line of symmetry

Any line splitting a shape into two parts such that the two parts are the same is called a line of symmetry. These parts are also said to be symmetrical to each other.

For instance, the image below shows a line of symmetry which splits the red outlined shape into two parts that are exactly the same.

Line of symmetry

Line of symmetry 1

Based on the above examples, we obtain the following observations:

  • The sides of the image split up by the line of symmetry, must look the same[c].

  • If we fold the paper (on which image is drawn) along the line of symmetry, each part of the image will completely overlap the other part.

 

The above observations will help us find the line of symmetry in any shape.

Example 1: Which of the following shapes does not have a line of symmetry?

Find the line of symmetry in any shape

 

Solution

If we fold both the papers from top to down as shown in A1 and B1, we get a line of symmetry in A but not in B. If we fold both the papers from left to right as shown in A2 and B2, we get no line of symmetries in both A and B.

Find the line of symmetry in any shape 1

 

Shapes with more than one lines of symmetry

Can we have more than one line of symmetry? The answer is yes. The table below shows some examples of shapes/figures with more than one line of symmetry.

image1 Image6 Image11
Image2 Image7 Image12
Image3 Image8 Image13
Image4 Image9 Image14
Image5 Image10 Image15

 

Real-life examples of symmetry

  • Reflection of trees in clear water and reflection of mountains in a lake.

  • Wings of most butterflies are identical on the left and right sides.

  • Some human faces are the same on the left and right side.

  • People can also have a symmetrical mustache.

Real-life examples of symmetry

 

Example 3: Which of the following is not a line of symmetry?

Not a line of symmetry

 

Answer:  (b) and (e) does not have a line of symmetry.

 

Example 4: Given below is a left part of a picture and its line of symmetry. Complete the picture.

Line of symmetry example 1

 

Solution:

The complete picture is as shown below.

Line of symmetry example 2

The other half should be exactly the same as the given half. We can use the grids to find the other half. We look at each vertex of the yellow part and measure its distance from the line of symmetry. Now we draw each vertex corresponding to the yellow part vertices on the purple section, keeping the distance from the line of symmetry.

 

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