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Lines of Symmetry

Home > By Subject > Geometry > Symmetry

Work through the lessons below to help your child to gain an understanding lines of symmetry and identify symmetrical, and non-symmetrical objects.

Learning Takeaways: After this lesson, students will be able to:

  • Identify whether a figure is symmetrical
  • Draw lines of symmetry on a figure
  • Complete a drawing over a line of symmetry

Identifying Symmetrical Figures

This section will help your child to identify whether a figure is symmetrical.

A figure is symmetrical if it can be split exactly in half. Look at the example below.

a symmetrical happy face with line of symmetry shown

Symmetry means that both sides are the exact same when split in half.

Notice that both sides of the happy face look exactly the same. That means this figure is symmetrical.

Look at the next example. Is this figure symmetrical? Does it look exactly the same on both sides of the line?

symmetrical octagon with line of symmetry marked arrow pointing to left

This octagon has more than 1 line of symmetry. Can you find the others?

The octagon is symmetrical. If you fold it where the line is, each side would match perfectly. But how do you know when a figure is NOT symmetrical? Look at the example below. This figure is not symmetrical. Can you figure out why?

a non-symmetrical figure arrow pointing to left

Both sides are not the same!

The lightning bolt is not symmetrical because it does not split in half with two equal sides. One simple way to see if a figure is symmetrical is to draw it on paper and fold it in half. If the sides match completely, it is symmetrical.

Drawing Lines of Symmetry

This section will help your child to draw lines of symmetry on a figure.

A line of symmetry divides a figure in half. Figures can have more than one line of symmetry.

Look at the square below. How many lines of symmetry do you count? Be careful to count each line only once!

square with all lines of symmetry shown

Does a rectangle have as many lines of symmetry as a square? Remember that a line of symmetry will split a figure in half so that each piece is exactly the same. Notice that the rectangle has two fewer lines of symmetry. Can you think of which direction the line of symmetry cannot go?

rectangle with both lines of symmetry marked

A rectangle cannot have a diagonal line of symmetry like a square because the sides are not the same length. If you fold this rectangle diagonally so that Corner A meets Corner D, the sides would not match. Try it with a piece of notebook paper!

You can draw lines of symmetry on many different figures. Look at the lines of symmetry on the figures below. Notice how different types of figures can have different numbers of lines of symmetry.

triangle with symmetry markedcrescent moon with symmetry marked    polygon with symmetry marked     heart shape with symmetry line shown

Creating Symmetrical Figures

This section will help your child to complete a drawing over a line of symmetry.

Look at the figure below. Only half of it is drawn. You can use the line of symmetry as your guide to draw the other half. Start with a point on the line of symmetry and draw the same thing on the other side.

a shape created through symmetry
  1. Make a horizontal line
  2. Make a vertical line
  3. Make a horizontal line
  4. Make a diagonal line

Figure A is the original drawing and figure B was drawn to be a symmetrical or identical part.

 

Symmetry Worksheets

You can click the links below and get your child to try the symmetry worksheets. These worksheets will help practice what is shown above.

Symmetry In Your Life (Activities)

Here is a list of activities that you can do at home or in your neighborhood to help understand symmetry.

  • Symmetry at the Supermarket
    • Go to the supermarket and identify symmetrical boxes, containers, and packages. 
    • Look at the different fruits and vegetables.  Which are symmetrical and which are not?  What is more likely to be symmetrical-fruit or veggies?
  • Symmetry in Nature
    • Examine flowers, trees, leaves for symmetry
    • Take a picture of an insect-where is the line of symmetry?
  • Symmetry in Your Bedroom
    • Identify lines of symmetry on your bed, TV, video game system, computer and closet door.
    • Who has more symmetrical figures in the bedroom-you or your sibling?  How many more symmetrical figures do you see?
  • Kitchen Symmetry
    • Use boxes or containers from the kitchen cupboards to create a symmetrical figure on either side of a line of symmetry (you can use a meter stick or a long piece of tape as the line of symmetry).
  • Neighborhood Scavenger Hunt
    • Look for examples of symmetry by simply walking around your neighborhood.
    • Record drawings or pictures of figures that are symmetrical.
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