NZ Level 3
topic badge
Identify line and rotational symmetries
Lesson

Symmetry

We are looking at two ways in which an object can display symmetry. To understand what symmetry means, we need to look at which type of symmetry we are referring to first.

 

Line symmetry

Line symmetry occurs when a shape or image is reflected across a line. It's as if you can fold the shape or image on that line and one side is an exact match of the other. When you look at the tree below, you can see that the vertical line creates two sides that are identical. This means the shape is symmetrical. 

Sometimes there may be more than one line of symmetry and we look at identifying multiple lines of symmetry in Video 1.

 

 

Rotational symmetry

If we turn a shape or object, and the original shape appears again, we say it has rotational symmetry. If you rotate this snowflake, will it look the same at any point? How many times it will look identical? 

In Video 2, we use a clever method to help identify rotational symmetry with our snowflake, as well as looking at a shape that doesn't have rotational symmetry.

Did you know?

Some shapes have both line and rotational symmetry and some shapes have neither line nor rotational symmetry! Other shapes might have one or the other.

 

Worked Examples

Question 1

Which of the following shapes have rotational symmetry? Select all that apply.

  1. A

    B

    C

    D

    E

    F

    G

    H

    A

    B

    C

    D

    E

    F

    G

    H

Question 2

What type of symmetry do the following shapes have?

  1. Line

    A

    Rotational

    B

    Neither

    C

    Both

    D

    Line

    A

    Rotational

    B

    Neither

    C

    Both

    D
  2. Line

    A

    Rotational

    B

    Neither

    C

    Both

    D

    Line

    A

    Rotational

    B

    Neither

    C

    Both

    D
  3. Line

    A

    Rotational

    B

    Neither

    C

    Both

    D

    Line

    A

    Rotational

    B

    Neither

    C

    Both

    D
  4. Line

    A

    Rotational

    B

    Neither

    C

    Both

    D

    Line

    A

    Rotational

    B

    Neither

    C

    Both

    D
  5. Line

    A

    Rotational

    B

    Neither

    C

    Both

    D

    Line

    A

    Rotational

    B

    Neither

    C

    Both

    D
  6. Line

    A

    Rotational

    B

    Neither

    C

    Both

    D

    Line

    A

    Rotational

    B

    Neither

    C

    Both

    D

Question 3

How many lines of symmetry does this figure have?

Outcomes

GM3-3

Classify plane shapes and prisms by their spatial features

What is Mathspace

About Mathspace