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9.03 Line and rotational symmetries


Are you ready?

Can you identify  lines of symmetry  in a shape? Look at the picture of a dog house below, is it symmetrical? Could you place a line through the picture so that the image on one side matches the image on the other?

A symmetrical dog house

The line of symmetry

If you can fold or cut a shape in half, and both sides look identical, we can say that shape has line symmetry. Let's learn more.

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Example 1

How many lines of symmetry does this painting have?

A circular pattern. Ask your teacher for more information.
Worked Solution
Create a strategy

Think of how many different lines can be drawn to split an object into two identical halves.

Apply the idea

Here is one of the lines of symmetry.

A diagonal dashed line is drawn through a circular pattern. Ask your teacher for more information.

Lines of symmetry can also be drawn horizontally, vertically, and diagonally the other way.

So there are 4 lines of symmetry.

Idea summary

If a shape is symmetrical, it means that when we draw a line through it, one side is identical to the other.

Some shapes or objects have more than one line of symmetry.

Rotational symmetry

If you can spin or turn a shape or object part the way around, and it looks identical, we can say the shape has rotational video. Watch this video to learn more.

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Example 2

Which of the following shapes have rotational symmetry?

A rectangle
A T-shaped polygon
A right trapezium
An upside down right trapezium
Worked Solution
Create a strategy

Imagine rotating the shape and see if it perfectly overlaps the original shape after a rotation that is less than 360\degree.

Apply the idea

Among the choices, the rectangle has rotational symmetry at 180\degree and 360\degree.

So, the correct answer is Option A.

Idea summary
  • Line symmetry means we can fold our image in half and it matches perfectly.

  • Rotational symmetry means there is at least one time where our shape looks identical, after turning it.



Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries

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