Line Symmetry

A Line of Symmetry is a line on a figure such that when the figure is folded along that line, both sides matches exactly. It is also known as a "Mirror Line" or "Axis of Symmetry".

The line of symmetry is usually drawn with a dotted line.

A figure has Line Symmetry if it has at least one line of symmetry.

Below are examples of figures with a line of symmetry.

The line of symmetry can be vertical, horizontal or diagonal (i.e. slanted at an angle) as shown in the diagram below.

Some figures do not have a line of symmetry, while some have one line of symmetry and others can have more than one line of symmetry (as shown in the diagrams below).

Line Symmetry (Test Yourself)

Activity 1



Activity 2



Activity 3



Activity 4



Activity 5



Activity 6



Game 1



Game 2

Line Symmetry (Applications)

Line symmetry can be found in our daily lives (e.g. in nature) and is often used in Art (e.g. designs).

Below are examples of line symmetry that can be found in nature.

Below are exmaples of line symmetry being used in Art (e.g. designs).

Rotational Symmetry

A figure has Rotational Symmetry if when it is rotated $< 360^\circ$ and it looks the same as its original figure.

The Order of Rotational Symmetry is the number of times the figure looks the same as its original figure when rotated $360^\circ$.

The diagram below shows a regular (i.e. equal sides) hexagon (i.e. 6-sided polygon) with rotational symmetry of order 6.

The figures below each has a rotational symmetry of order 4.

The diagrams below show some examples of figures with rotational symmetry and their order of rotational symmetry.

Click on the "play" buttons ($\triangleright$) below to see the animation of the figures being rotated $360^\circ$.


Click on the "rotate" buttons, followed by the "starting point" dots to see the animation of the figure being rotated $360^\circ$.



Click on the "start" button on the interactive activity below, followed by the "open instructions" tab at the bottom of the interactive activity.



Choose a topic and click on it.

Rotational Symmetry (Test Yourself)

Activity 1

For the figure shown below, guess the order of rotation symmetry.
Click on the grey rectangles to check your answer.
To rotate the figure, click on the top "$\triangleright$".
To change to another figure, click on the bottom "$\triangleright$".



Game 1

Rotational Symmetry (Applications)

Rotational symmetry can be found in our daily lives (e.g. in nature) and is often used in Art (e.g. designs).

Below are examples of rotational symmetry that can be found in nature.

Below are examples of rotaional symmetry used in Art (e.g. designs).

Line & Rotational Symmetry (Test Yourself)

Scroll down to the "Exercises" section.



Discussion Questions

The diagram below shows how parallelograms, rectangles, rhombuses and squares are related.

A square is both a rectangle and a rhombus.
Rectangles and rhombuses are parallelograms.

We know that:

• A Rectangle has 2 lines of symmetry and a rotational symmetry of order 2.
• A Square has 4 lines of symmetry and a rotational symmetry of order 4.

1. How many line of symmetry does a Parallelogram has? And, what is its order of rotational symmetry?
2. How many line of symmetry does a Rhombus has? And, what is its order of rotational symmetry?

Instructions

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• Please post your answers to the above discussion questions in the comment section below. If the comment section is not displayed, please click on the "comments" link below.
[1 bonus point for posting each of your answer to the discussion questions above]
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