Rotational symmetry and transformations

This chapter talks about line symmetry, rotational symmetry and transformations, and surface area of 3-dimensional shapes. We will learn how to find the lines of symmetry in 2-dimensional shapes, and whether a 2-dimensional shape has rotational symmetry. Also, we will learn how symmetry can help us find surface area of 3-dimensional shapes.

Symmetry can be found all around us. The fact that we are learning symmetry now is because our ancestors were so amazed by the symmetry in nature that a stream of study was developed!

A line of symmetry is a line that divides an object into two and produces two mirror images of each other. The lines of symmetry can be in any directions: horizontal, vertical or diagonal. An object can have more than one line of symmetry. The number of lines of symmetry varies in different polygons.

In the second part of the lesson, we will then explore rotational symmetry in 2-dimensional shapes. To say a figure has rotational symmetry means that when this figure turns about its centre of rotation, it will still look the same after a certain amount of rotation. Different shapes have different order of rotation and angle of rotation. Order of rotation refers to the number of times that the figure looks the same in one complete turn; while the angle of rotation is the smallest angle that the figure needs to turn so that it still looks the same. Like the line of symmetry, the order and angle of rotation can be different in different polygons too. For example, a regular hexagon has an order of rotation of 6 and its angle of rotation is 60°.

The last part of this lesson focuses on how to find the surface area of 3-dimensional shapes. Surface area is the total area of all faces of a shape. Thanks to our ancient mathematicians, we have formulas to help us find surface areas of many regular objects.

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Rotational symmetry and transformations

When an object is turned around its center of rotation to certain degrees and the object looks the same, we can say it has rotational symmetry. We will learn the details of rotational symmetry including, lines of symmetry, order of rotation, and angle of rotation.


  • 2.
    All of the following figures have rotation symmetry.
    • Where is the centre of rotation?
    • What are the order and the angle of rotation? Show your answers in degrees and as fraction of a turn.
  • 3.
    What are the number of lines of symmetry and the order of rotation?
    • a)

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Rotational symmetry and transformations

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