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Symmetry

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Basics on the topic Symmetry

Symmetry – Meaning

If an object is defined as symmetric, it means that if you split the object, it has two exactly matching parts. This means that you could put a mirror to this object and one half is the exact image of the other half. In this text, you’ll be able to learn all about symmetry and lines of symmetry.

Lines of Symmetry – Definition

What does symmetry mean? Let’s start with the line of symmetry definition. A line of symmetry is a real or imaginary line that divides a shape into two mirror images.

If an object is symmetrical, it has one or more lines of symmetry. Fun fact: some objects have infinite lines of symmetry, such as a circle! We can’t measure the lines of symmetry in a circle, because there are too many!

How do you explain the difference between symmetry and asymmetry? It’s very simple. If an object has no lines of symmetry that means it is asymmetrical. If an object has one or more lines of symmetry then it is symmetrical.

Lines of Symmetry – Examples

How do you check if a given shape or object is symmetrical or not? When looking at a shape ask yourself:

  • Is there at least one line of symmetry?
  • What is the line of symmetry?

Let’s look at this example. How many lines of symmetry does a star have? First remember the symmetry definition or symmetry meaning to keep in mind how symmetry works.

line_13.svg

We can check the lines of symmetry by folding a shape in half, if there is a line of symmetry each side will match!

line_14.svg

Lines of Symmetry – Summary

So, what is a line of symmetry in maths? A line of symmetry is a real or imaginary line that divides a shape into two mirror images.If an object is symmetrical, it has one or more lines of symmetry. If you want to find out more about terms such as reflective symmetry, rotational symmetry and butterfly symmetry, there are many symmetry activities and symmetry worksheets to further build on your knowledge on this website.

Frequently Asked Questions regarding Symmetry

What does symmetry mean in maths?
What is a line of symmetry?
What is a mirror line?
How many lines of symmetry does an object need to be symmetric?

Transcript Symmetry

Nico and Nia are speechless! Wow! Look at all of the amazing shapes Nico and Nia can see! "Wow, this is so cool!" "Do you think these shapes are symmetrical?" "What does symmetrical mean?" "If a shape is symmetrical, that means it has one or more lines of symmetry. If a shape has no lines of symmetry we say that it is asymmetrical." "Oh okay. Hmm I'm not sure about these shapes!" Let's help Nico and Nia determine if the shapes are symmetrical or asymmetrical by identifying "Lines of Symmetry". A "line of symmetry is a real or imaginary line that divides a shape into two regions, or parts, that are MIRROR IMAGES of each other across the line." Mirror images means that both sides are EXACTLY the same. A line of symmetry can be in any direction, AND shapes and objects can have more than one line of symmetry. We can check the lines of symmetry by folding a shape in half. If there is a line of symmetry each side will match! Shapes that have one or more lines of symmetry are SYMMETRICAL. Shapes that have no lines of symmetry are ASYMMETRICAL. For example, we can divide the satellite into two mirror images with a line of symmetry HERE. We can check the line of symmetry by folding it on the line. As you can see both sides match! Does it have more than one line of symmetry? We can also draw a line of symmetry HERE, and we can see that when we fold it both sides match. Since the satellite has two lines of symmetry, it is a SYMMETRICAL shape. Let's help Nico and Nia sort some other shapes. Is the alien SYMMETRICAL or ASYMMETRICAL? The alien is SYMMETRICAL because we can draw a line of symmetry HERE, and when we fold it both sides match. Let's try and draw a line of symmetry this way. Does this work? Since both sides are not exactly the same, this is not correct. The alien has only ONE line of symmetry and is a SYMMETRICAL shape. Now, let's look at the moon. Try finding a line or some lines of symmetry on your own. What do you notice about the moon? This picture of the moon is a circle that has many lines of symmetry! In fact, a circle has so many lines of symmetry we say it has INFINITE, or endless, lines of symmetry! Is this picture of the moon SYMMETRICAL or ASYMMETRICAL? The moon is SYMMETRICAL. Let's look at the alien spaceship. Is it symmetrical or asymmetrical? It is symmetrical because we can draw one line of symmetry HERE. What about the meteor? Is it SYMMETRICAL or ASYMMETRICAL? Even though the meteor is kind of round, the craters along the outside are not mirrored exactly on the opposite sides. The meteor has no lines of symmetry, so it is ASYMMETRICAL. What about the bear on the skateboard? Is it SYMMETRICAL or ASYMMETRICAL? The bear on the skateboard is ASYMMETRICAL because each side is not a mirror image. Remember, a line of symmetry is a real or imaginary line that divides a shape into two regions, or parts, that are mirror images of each other across the line. A line of symmetry can be in any direction, AND shapes and objects can have more than one line of symmetry. Shapes that have one or more lines of symmetry are SYMMETRICAL. Shapes that have no lines of symmetry are ASYMMETRICAL. "Wait a second. What was that bear doing in outer space?!" "Never mind that! The meteor is heading right for our ship!" "Don't worry, it was just the pillow!"

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Symmetry exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Symmetry.
  • How many lines of symmetry are there?

    Hints

    Remember, lines of symmetry can be checked by folding a shape in half with an imaginary line where both sides match.

    Check to see if there is more than 1 line of symmetry.

    Solution

    There are 2 lines of symmetry for this object. When we imagine folding it where the lines are, both sides match.

  • Highlight the objects that are symmetrical.

    Hints

    Remember, lines of symmetry can be checked by folding a shape in half with an imaginary line where both sides match.

    When imagining folding the object in half, look closely at the parts that won't match up.

    Solution

    The moon, star, and alien spacecraft are symmetrical. We know this because when folding the objects along an imaginary line, the sides mirror each other.

    The alien, bear, and meteor are asymmetrical. We know this because when folding the objects along an imaginary line, the sides do not mirror each other.

  • Symmetrical or asymmetrical?

    Hints

    Remember, symmetrical means the object has at least 1 line of symmetry and asymmetrical means the object has no lines of symmetry.

    Remember, lines of symmetry can be checked by folding a shape in half with an imaginary line where both sides match.

    When imagining folding the object in half, look closely at the parts and images that won't match up.

    Solution

    The moon, star, and space ship are symmetrical because when imagining folding the object in half where the lines are, both sides and images match.

    The alien, Earth, and meteor are asymmetrical because when imagining folding the object in half, both sides and images do NOT match.

  • How many leaves are symmetrical?

    Hints

    Remember, lines of symmetry can be checked by folding a shape in half with an imaginary line where both sides match.

    When imagining folding the object in half, look closely at the parts that won't match up or stick out.

    Solution

    There are 4 symmetrical leaves. These leaves are circled in green. When folding these leaves along the imaginary line, both sides are exactly the same, so they are symmetrical.

  • What is a line of symmetry?

    Hints

    The dotted line on this alien shows a line of symmetry.

    This bear does not have a line of symmetry.

    Solution

    A line of symmetry is a real or imaginary line that divides a shape into two regions, or parts, that are mirror images of each other across the line.

    For example, this spaceship is symmetrical and has a line of symmetry where the dotted line is.

  • How many lines of symmetry?

    Hints

    Remember, lines of symmetry can be checked by folding a shape in half with an imaginary line where both sides match.

    When imagining folding the object in half, look closely at the parts that won't match up.

    Check to make sure that you've found all lines of symmetry.

    Solution

    The sun has 8 lines of symmetry. When we imagine folding it where the lines are, both sides match. _________________________________________________________________________________

    The umbrella has 1 line of symmetry because when imagining folding the object in half, both sides match.

    The palm tree has 0 lines of symmetry because when imagining folding the object in half, both sides do NOT match.

    The gold fish has 1 line of symmetry because when imagining folding the object in half, both sides match.

    The octopus has 0 lines of symmetry because when imagining folding the object in half, both sides do NOT match.

    The star has 5 lines of symmetry because when imagining folding the object in half, both sides match.