# Lines of Symmetry

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Lines of Symmetry
CCSS.MATH.CONTENT.4.G.A.3

## Symmetry and Lines of Symmetry

If an object is symmetric, it means that if you split an 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

Let’s start with the definition of the term line of symmetry. A line of symmetry is a real or imaginary line that divides a shape into two mirror images. What is a mirror line? Mirror line is just another word for symmetry line.

If an object is symmetric, 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 types of lines of symmetry that means it is asymmetric or asymmetrical. If an object has one or more lines of symmetry then it is symmetric or 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 definition of symmetry or symmetry meaning to keep in mind how symmetry works.

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

## Symmetry – Applications

How is symmetry useful? You may be wondering why symmetry is important or why symmetry matters. There are a few places where symmetry is used in real life. Where can symmetry be found? Artists use symmetry when drawing or making other forms of art. It is also used in architecture and construction. Even people have facial symmetry because each half of our face often mirrors the other! Think about other ideas about where symmetry is found, it may surprise you!

## Lines of Symmetry – Summary

A line of symmetry is a real or imaginary line that divides a shape into two mirror images. What is a mirror line? Mirror line is just another word for symmetry line. If an object is symmetric, it has one or more lines of symmetry. How many lines of symmetry does a rectangle have? And how many lines of symmetry does a square have? On this website you can find symmetry and types of symmetry. You’ll also find worksheets, activities, and exercises.

## Frequently Asked Questions regarding Symmetry

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

### TranscriptLines of Symmetry

[excited][Nico and Nia are in space]Nico and Nia are speechless! Wow! Look at all the amazing shapes Niko and Nia can see! [Nico: Steve][Excited] "Wow, this is so cool!" [Nia: Lena] "Do you think these shapes are symmetric or asymmetric?" [Nico: Steve] "What does symmetric and asymmetric mean?" [Nia: Lena] "If a shape is symmetric, that means it has one or more lines of symmetry... and if it is asymmetric it has no lines of symmetry." [Nico: Steven][Thinking] "Oh okay(...) hmm I'm not sure about these shapes!" Let's help Nico and Nia determine if the shapes are symmetric or asymmetric by identifying(...) [title] "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 SYMMETRIC. Shapes that have no lines of symmetry are ASYMMETRIC. 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 SYMMETRIC shape. Let's help Nico and Nia sort some other shapes. Is the alien SYMMETRIC or ASYMMETRIC? (...) The alien is SYMMETRIC 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 SYMMETRIC 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? (...) 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 the moon SYMMETRIC or ASYMMETRIC? (...)

jj It is symmetric because we can draw one line of symmetry HERE. What about the meteor (...) is it SYMMETRIC or ASYMMETRIC? (...) 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 ASYMMETRIC. What about the bear on the skateboard (...) is it SYMMETRIC or ASYMMETRIC? The bear on the skateboard is ASYMMETRIC 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 SYMMETRIC.

[Nico:Steven ][alarmed/confused] "Wait a second(...)what was that bear doing in outer space?!" [Nia:Lena ] [scared/urgent] "Nevermind that! The meteor is heading right for our ship!" [Nico: Steven ][Nico and Nia are back in the attic] "Don't worry, it was just the pillow!"

## Lines of Symmetry exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Lines of 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 symmetric.

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 symmetric. We know this because when folding the objects along an imaginary line, the sides mirror each other.

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

• ### Symmetric or asymmetric?

Hints

Remember, symmetric means the object has at least 1 line of symmetry, and asymmetric 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 symmetric because when imagining folding the object in half where the lines are, both sides and images match.

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

• ### How many leaves are symmetric?

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

• ### 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 symmetric 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.