Change the line of reflection using the dropdown menu and drag the line of reflection.

What do you notice as you drag each line of reflection?

A figure has **line symmetry** (sometimes called **reflection symmetry**) if one half of the figure is the reflection of the other. This is equivalent to there being a line of reflection which maps a figure onto itself.

We can create a shape that has line symmetry using the reflection transformation.

How many lines of symmetry does the following figure have?

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Determine the lines of symmetry for the square.

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Idea summary

A figure has line symmetry if one half of the figure is the reflection of the other.

If a rotated shape perfectly overlaps the original shape after a rotation that is less than 360\degree, then the original shape has **rotational symmetry**. The point about which this rotation happens is called the **center of rotation**.

Change the shape using the dropdown menu and click the 'Rotate 180 degrees' box to rotate the figure. Click 'Reset' to return the figure to its origianl position.

What do you notice as you rotate each shape 180\degree?

A specific rotational symmetry called **point symmetry** occurs when a figure is unchanged after a 180 \degree rotation.

Each point in a figure with point symmetry has a matching point the same distance from the central point, but on the *opposite* side.

This makes the central point of rotation a midpoint for each point and its image.

Notice that some figures have only point symmetry, or only line symmetry, but not both.

Point symmetry only

Line symmetry only

While other figures have both line and point symmetry, or no symmetry at all.

Both point symmetry and line symmetry

No symmetry

For each figure, determine the type(s) of symmetry present.

a

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b

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c

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d

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e

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Determine whether each of the following statements is true about the quadrilateral shown.

a

y=0 is a line of symmetry.

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b

The quadrilateral has point symmetry.

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Idea summary

A figure with point symmetry remains unchanged after a 180 \degree rotation.

The point of rotation for a figure with point symmetry acts as a midpoint for each point and its matching opposite.