This document discusses different types of symmetry found in shapes, letters, numbers, objects, and designs. It provides examples of rotational symmetry, including some letters that have order 2 rotational symmetry like H, I, O, and Z. It also gives examples of shapes, flags, road signs, buildings and monuments that demonstrate various kinds of line and rotational symmetry.

2. Symmet
ry
Lines of symmetry
2
1
Order of Rotation
2
4

3. Common Errors
• There are some examples of shapes that are tricky when
considering symmetry. A typical parallelogram actually cannot be
folded in half even though it appears to have two 'equal halves'.
• We can see both kinds of symmetry
around us; rotational as well as
line symmetry.

4. Letters and Line Symmetry.
A B C D E H I M O
T U V W X Y
There are some letters which do
not have any line of symmetry.
FGJKLNPQSZ

5. N
Letters and Rotational Symmetry.
X
rotation
al
symmetry
at order
1
H
rotational
symmetry
at order 2
I
O
rotational
symmetry at
order 2
rotational
symmetry at
order 2
rotational
symmetry
at order 2
Z
S
rotational
symmetry at
order 1
rotation
al
symmetry
at order

6. • This flower has 1 line
of symmetry and a
rotational symmetry
of Order 5 as it
matches itself 5
times.
Nature & Line Symmetry.

7. Road Signs &
Symmetry.
Order 3+0 lines of symmetry.
Order 2+1 line of symmetry.
Order 3+0 line of symmetry.
Order 4+4 lines of symmetry
Order 2+0 line of symmetry.
Order 1+1 line of symmetry.

8. Monuments & Symmetry.
Symmetry exists in
architecture all around
the world.
One of the best known
examples of this is the
Taj Mahal.
If an object is reflected in water
many people believe
the image has line symmetry.
But is it really a 'mirror image'? Is it
really symmetrical?
What are your thoughts?
The image can be rotational
symmetry.

9. Flags & Line
Symmetry.
Japan
Micronesia
Finland
Indonesia
United Nations
Aboriginal Flag of Australia
Canada
British

10. Rotational symmetryyes(2)
Rotational symmetryyes(2)
Rotational symmetryyes(1)
Flags and Rotational
Symmetry.
Rotational symmetryyes(1)
Rotational symmetryyes(1)
Rotational symmetryyes(1)
Rotational symmetryyes(1)
Rotational symmetryyes(2)

11. Math symbols & Symmetry.

12. Masks,tatt
oos &
Symmetry.

13. Religious Symbols & Symmetry.
L.S-1
R.S-0
L.S-1
R.S-0
The Memorah is used during
the Jewish feast of Chanukah.
L.S-4
R.S-8 Muslim buildings often
have symmetry.
The Dharma Wheel is a
Buddhist symbol.
L.S-6
R.S-6
The Jewish Star of David.
L.S-1
R.S-0
L.S-Line of Symmetry
R.S-Rotational Symmetry
The Christian Cross

14. Words &
rotational
symmetry.

15. Objects & Rotational
Symmetry.
•
Order 5
Often the picture
cards in a playing
deck have
rotational
symmetry.
Order 7
•
Order 2
Since all the toppings
are placed so evenly, this pizza
has rotational symmetry of
Order 6.

16. 
Click on the shapes to see how many lines of symmetry they have.