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Symmetrical Figures / Shapes

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Basics on the topic Symmetrical Figures / Shapes

Types of Symmetry

Today we’re going to learn about two types of symmetry. Let’s review what symmetry is. 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! If an object has no types of symmetry that means it is asymmetrical. What are the different types of symmetry? The next section has more information on types of symmetry in maths.

Types of Symmetry – Overview

We differentiate between reflective symmetry and rotational symmetry.

Reflective symmetry is when one half of the object or shape reflects the other half.

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Rotational symmetry is when a shape or object is rotated or turned around a central point and looks exactly the same.

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Types of Symmetry – Summary

Now you know about some types of symmetry in geometry; reflective and rotational symmetry. The following table shows a short overview of the two types of symmetry which we learned about.

Type of Symmetry Explanation
Reflective symmetry One half of the object or shape reflects the other half.
Rotational symmetry A shape or object that can be rotated or turned around
a central point and looks exactly the same.

See if you can spot any symmetry around you or any different types of symmetry in nature. Want to practice more? On this website you can find rotational and reflective symmetry interactive activities as well as reflective symmetry worksheets and rotational symmetry worksheets.

Frequently Asked Questions concerning Types of Symmetry

What are the types of symmetry in geometry?
What is reflective symmetry?
What is rotational symmetry?

Transcript Symmetrical Figures / Shapes

"I'm sooo bored Nico!" "Look what I found!" "Different types of symmetry?" "It seems when we spy an object with a certain type of symmetry, it will lead us to another clue!" Let's help Nico and Nia by identifying objects with "Different Types of Symmetry". 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 an object has NO symmetry, that means each half will not be a mirror image, so it is ASYMMETRICAL. The first clue says to find an object with reflective symmetry. Reflective symmetry is when one half of the object or shape reflects the other half, and it is the most common type of symmetry. This smiley face has REFLECTIVE symmetry, since the right side is an EXACT reflection of the left.

Nico and Nia find a sandcastle. Does the sandcastle have reflective symmetry? No. Each half does NOT reflect exactly, so the sandcastle is ASYMMETRICAL.

What about THIS butterfly, does it have reflective symmetry? Yes, the butterfly DOES have reflective symmetry because each half is mirrored.

Another clue asks Nico and Nia to find an object with rotational symmetry. Rotational symmetry is when a shape or object is rotated or turned around a central point and looks exactly the same. One example is the sun, because when it is rotated around the central point HERE it looks exactly the same. Nico and Nia find a bird. Does it have rotational symmetry? No, the bird does NOT have rotational symmetry because when it is rotated around the central point HERE it does NOT look exactly the same. What about this pinwheel does it have rotational symmetry?

Yes, the pinwheel does have rotational symmetry because when it is rotated around the central point HERE it looks the same. Nico and Nia have found different types of symmetry. Before we see what they do next, let's summarise. Remember, a line of symmetry is a real or imaginary line that divides a shape into two mirror images. We have looked at two different types of symmetry. Reflective symmetry is when one half of the object or shape reflects the other half. Rotational symmetry is when a shape or object is rotated or turned around a central point and looks the same. "Wait a second Nico! I spy paper and ink in your bag. Did YOU create this game?!" "Well, didn't you say you were bored?" "Thanks Nico! There's just one problem, I'm bored again!"

Symmetrical Figures / Shapes exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Symmetrical Figures / Shapes.
  • Reflective symmetry.

    Hints

    This flag can be reflected in two ways: it can be folded along the dotted lines, and will be a mirror image of itself.

    Remember, shapes can be reflected horizontally, vertically or diagonally.

    Solution

    4 of these shells have reflective symmetry. If these shells were folded along the dotted line, they would be a mirror image of themselves.

  • Types of symmetry.

    Hints

    Shapes with only reflective symmetry can have either vertical, horizontal or diagonal lines of symmetry.

    Does the whale have a line of symmetry? Does it have a mirror image either side of the fold line?

    Solution

    The windmill has rotational symmetry. It can be rotated around the central point and still look the same.

    The flower has rotational symmetry. It can be rotated around the central point and still look the same.

    The turtle has reflective symmetry. It has one vertical line of symmetry.

    The flag has reflective symmetry. It has one horizontal line of symmetry.

    The dolphin is asymmetrical. There are no mirror images that could be seen by a fold or mirror line.

    The shell is asymmetrical. There are no mirror images that could be seen by a fold or mirror line.

  • Types of symmetry.

    Hints

    Remember, a shape has rotational symmetry if it can be rotated (turned) and still look the same as the original image.

    Does the shape have reflective symmetry only? Can it be folded and have a mirror image, but not look the same when rotated.

    Start by finding the shapes that are asymmetrical, then the shapes with rotational symmetry, then the shapes with reflective symmetry only.

    Solution

    The octopus, the crab, and the green shell have reflective symmetry only.

    The orange shell and both fish are asymmetrical.

    The beachball and the starfish have rotational symmetry.

  • Lines of symmetry.

    Hints

    How many ways can the shape be folded and have an exact mirror image either side of the fold line?

    When a shape is symmetrical, it has a mirror image. It would have to fold exactly in half and the sides meet perfectly.

    A rectangle cannot fold diagonally and have the sides meet exactly, so a rectangular shape cannot have a diagonal line of symmetry.

    Solution

    Each pair of beach towels has the same number of lines of symmetry.

  • Identify rotational symmetry.

    Hints

    When a shape has rotational symmetry, it can be rotated (turned) and will still look the same as the original shape, like this flower.

    Imagine rotating (turning) the shape. Does it look the same?

    Solution

    The only image with no rotational symmetry is the crab. If the crab was rotated, it would look different than the original image.

  • Assigning shapes.

    Hints

    Try to imagine folding the shape in half along an imaginary fold line. If the sides match up exactly, it has a line of symmetry.

    Solution

    The palm tree and the sailing boat have 0 lines of symmetry.

    The beach hut, the surfboard, the ice-cream, and the sunglasses have 1 line of symmetry.

    The rowing boat has 2 lines of symmetry.

    The sun and the ship's steering wheel have more than 2 lines of symmetry.