Symmetry: A Visual Presentation        

Line Symmetry Shape has line symmetry when one half of it is the mirror image of the other half. Symmetry can have vertical, horizontal or diagonal line symmetry.         How would you define the term 'line symmetry'?         Why might some people see line symmetry as a thing of beauty?

Is a butterfly symmetrical?

Line Symmetry exists in nature but you may not have noticed.

At the  beach there are a variety of shells with vertical line symmetry.

Under the sea there are also many symmetrical objects such as these crabs. They have horizontal symmetry. This starfish has vertical and diagonal symmetry. This type of symmetry is also called reflectional symmetry as the two parts reflect/match along each side of a dividing line ( or axis ).

Animals that have Line Symmetry Here are a few more great examples of vertical symmetry in the animal kingdom.

THESE MASKS HAVE SYMMETRY These masks have a line of symmetry from the forehead to the chin.   The human face also has a line of symmetry in the same place.

REFLECTION IN WATER If an object is reflected in water it is considered to have line symmetry along the waterline. This is called horizontal symmetry.

The Taj Mahal In this view of the building there is a line of symmetry through the centre of the tomb from top to bottom. It was completed in 1630 by the Indian ruler Shahs Jahan as a tomb for his favourite wife Mumtaz Mahal who died as a result of giving birth to their 14th child. To build this tomb it took 20 000 workers, 20 years (Encarta 97) and it is rumoured that they used 40 000 elephants to transport the materials. Symmetry exists in architecture all around the world.  The best known example of this is the Taj Mahal.

This photograph shows 2 lines of symmetry This photograph shows 2 lines of symmetry. One vertical, the other horizontal along the waterline. (Notice how the prayer towers, called minarets, are reflected in the water and side to side).

Let’s look at 2D shapes to find lines of symmetry. 2D Shapes and Symmetry Let’s look at 2D shapes to find lines of symmetry.  

How many lines of symmetry did you find for each shape?

An equilateral triangle has 3 lines of symmetry.

A square has 4 lines of symmetry.

A regular pentagon has 5 lines of symmetry.

A regular hexagon has 6 lines of symmetry .

A regular octagon has 8 lines of symmetry. Is there a pattern here?             How could you prove that a square really does have 4 lines of symmetry and not 2.             A rectangle has 4 lines of symmetry. True or False? How could you prove it?             What pattern can you see emerging on this page?

Let’s do a practice problem together: Lisa and Rob are flying a rhombus shaped kite. They need to fold the kite in half along a line of symmetry to have it fit in a backpack. Which picture shows the lines they can choose from? A B C D

D