Different Types of Symmetry

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Contents

What are the Types of Symmetry?

Nico and Nia are at the beach when Nico finds a piece of paper that leads to a scavenger hunt. Their job is to find objects with different types of line symmetry at the beach. After they are finished, Nia discovers that Nico was behind the different types of symmetry scavenger hunt all along!

What is Symmetry in Math?

Let’s review the symmetry definition. A line of symmetry is a real or imaginary line that divides a shape into two mirror images. 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! If an object has no types of lines of symmetry that means it is asymmetric. What types of symmetry can a shape have? The next section has more information on how many types of symmetry are there and details and answers the basic question: what are the 3 basic types of symmetry?

Three Types of Symmetry

What are the three types of symmetry? There are 3 types of symmetry: reflective symmetry, translational symmetry, and rotational symmetry.

Reflexive symmetry, or reflection symmetry, is when one half of the object or shape reflects the other half.

reflection-symmetry-line-of-symmetry-middle-of-smiley-face-types-of-symmetry.svg

Translational symmetry, or translation symmetry, is when a shape or object creates a pattern the same direction and same distance apart.

translation-symmetry-line-of-symmetry-diving-each-row-of-flowers-four-rows-of-three-types-of-symmetry.svg

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

rotation-symmetry-line-of-symmetry-sun-with-central-point-in-the-middle-types-of-symmetry.svg

Summary for What Types of Symmetry are There?

Now that you know the different types of symmetry, you can answer ‘what are the different types of symmetry’ easily! Remember, there are 3 types of symmetry: reflective symmetry, translational symmetry, and rotational symmetry.

Want to practice more with the question ‘what are the 3 types of symmetry’? On this website you can find different types of symmetry worksheets, activities, and exercises.

Transcript Different Types of Symmetry

[Nia: Lena] [Yawns] "I'm sooo bored Nico!" [Nico: Steve][excited] "Look what I found!" [Nico: Steve] [Looks at paper] "It says, 'I spy with my little eye (...) [confused] different types of symmetry?" [Nico: Steve] "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 [title] "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 symmetric, 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 (...) ASYMMETRIC. The first clue says to find an object with reflexive symmetry. Reflexive 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 REFLEXIVE symmetry, since the right side is an EXACT reflection of the left.

Nico and Nia find a sandcastle. Does the sandcastle have reflexive symmetry? (...) No, each half does NOT reflect exactly, so the sandcastle is ASYMMETRIC. [no vo] What about THIS butterfly, does it have reflexive symmetry? (...) Yes, the butterfly DOES have reflexive symmetry because each half is mirrored. The next clue wants them to find an object with TRANSLATIONAL symmetry. Translational symmetry is when a shape or object creates a pattern in the same direction AND the same distance apart. One example is the pattern HERE, (...) since the flowers are all in the same direction and same distance apart.

[Goes back to Nico and Nia looking around] Nico and Nia find a pattern on a beach towel. Does the pattern have translational symmetry? (...) No, the beach towel does NOT have translational symmetry because the stars are not all in the same direction and same distance apart. What about THIS pattern on the ice cream stand? Does this pattern have translational symmetry? (...) Yes, the ice cream cones have translational symmetry because they create a pattern in a certain direction AND a certain distance apart. The last clue wants them 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? (...) [no vo] Yes, the pinwheel does have rotational symmetry because when it is rotated around the central point HERE it looks exactly the same. Nico and Nia have found all the different types of symmetry. Before we see what they do next, let's summarize. Remember (...) a line of symmetry is a real or imaginary line that divides a shape into two mirror images. There are three different types of symmetry. Reflexive symmetry is when one half of the object or shape reflects the other half. Translational symmetry is when a shape or object creates a pattern the same direction and same distance apart. Rotational symmetry is when a shape or object is rotated or turned around a central point and looks exactly the same. [Nia: Lena] [excited/suspicious] "Wait a second Nico! (...) I spy paper and ink in your bag (...) Did YOU create this game?!" [Nico: Steve] "Well, didn't you say you were bored?" [Nia: Lena] "Thanks Nico! There's just one problem (...) I'm bored again!"

Different Types of Symmetry Exercise

Would you like to practice what you’ve just learned? Practice problems for this video Different Types of Symmetry help you practice and recap your knowledge.
  • Reflexive symmetry.

    Hints

    This flag can be reflected 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 reflexive symmetry. If these shells were folded along the dotted lines they would be a mirror image of themselves.

  • Types of symmetry.

    Hints

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

    Does the whale have a line of symmetry?

    Remember, objects with rotational symmetry can be rotated around a central point and still look the same, like this object.

    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 reflexive symmetry. It has one vertical line of symmetry.

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

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

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

  • Types of symmetry.

    Hints

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

    Does the shape have reflexive 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 reflexive symmetry only.

    Solution

    The octopus, the crab and the blue shell have reflexive symmetry only.

    The 3 different beach towels have translational symmetry.

    The beachball and the starfish have rotational symmetry.

  • Lines of reflexive symmetry.

    Hints

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

    When a shape is symmetrical it would have to fold exactly in half and the sides match up perfectly in a mirror image.

    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 sail boat have 0 lines of symmetry.

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

    The row boat has 2 lines of symmetry.

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