This document discusses different types of symmetry including line symmetry, rotational symmetry, and reflection symmetry. It provides examples of symmetrical shapes in nature like shells, stars, and animals. Regular polygons like triangles, squares, pentagons and hexagons are used to demonstrate how many lines of symmetry and rotational order they have. Other concepts explained include reflection, translation, and rotational symmetry in different shapes. Real-world examples of symmetry in architecture, road signs, and masks are also presented.

1. Symmetry:
A Visual Presentation

2. Symmetry

3. To be a line of symmetry, the
shape must have two halves
that match exactly.
When you trace a heart onto a
piece of folded paper,
and then cut it out, the two half
hearts make a whole heart.
The two halves are symmetrical.

4. Line Symmetry
 Shape has line symmetry when one half
of it is the mirror image of the other half.
 Symmetry exists all around us and many
people see it as being a thing of
beauty.

5. Is a butterfly symmetrical?

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

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

8. Under the sea there are also
many symmetrical objects
such as these crabs
and this starfish.

9. Animals that have Line
Symmetry
Here are a few more great examples of
mirror image in the animal kingdom.

10. Line Symmetry in the Alphabet
Which letters have got lines of symmetry?
A B C D E F G H I
J K L M N O P Q R
S T U V W X Y Z

11. Lines of Symmetry all around us
Which of these road signs have got lines of
symmetry?

12. 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.

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

14. The Taj Mahal
Symmetry exists in architecture all around
the world. The best known example of
this is the Taj Mahal.

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

16. 2D Shapes and Symmetry
After investigating the following
shapes by cutting and folding,
we found:

17. an equilateral triangle has 3 internal
angles and 3 lines of symmetry.

18.
a square has 4 internal angles and 4
lines of symmetry.

19. a regular pentagon has 5 internal
angles and 5 lines of symmetry.

20. a regular hexagon has 6 internal angles
and 6 lines of symmetry .

21.
a regular octagon has 8 internal angles
and 8 lines of symmetry.

22. How many lines of symmetry to
these regular polygons have?
Do you
see a
pattern?

23. What about these math symbols?
Do they have symmetry?

24. Which of these flags have a
line of symmetry?
United States of Canada
America
Maryland England

26. Click the
triangle to
Turning a
see rotation
figure around a
point or a
vertex

27. What is Rotational Symmetry?
An image has Rotational
Symmetry if there is a point
in the image that the image
can be turned around a
certain number of degrees
and still look the same.

28. How do you determine if an
image has rotational
symmetry?
1. Trace the image.
2. Rotate the image until it
matches up exactly.
3. Continue until you reach
your starting point.

29. Rotational Symmetry is
described by identifying the
order of the figure.
This triangle has
an order of 3
because there are
3 positions where
the triangle looks
the same.

30. What is
the
order for
this
figure?

31. Rotational Symmetry
2
The order of
rotational
symmetry that
an object has is
the number of
1
Order times that it fits Order
3 on to itself
2
1 during a full
rotation of 3600
2 1
Order
3

32. Rotational Symmetry
What is the order of rotational symmetry of the shape below?

33. Rotational Symmetry
What is the order of rotational symmetry of the shape below?
5
4 1
3 Order 2
5

34. Rotational Symmetry
What is the order of rotational symmetry of the shape below?

35. Rotational Symmetry
What is the order of rotational symmetry of the shape below?
6
5 1
4 2
3
Order
6

36. Equilateral Triangle
An equilateral triangle has rotational symmetry of order ?

37. Equilateral Triangle
An equilateral triangle has rotational symmetry of order ? 3
3
2 1

38. Regular Pentagon
A regular pentagon has rotational symmetry of order ?
Pentagon

39. Regular Pentagon
A regular pentagon has rotational symmetry of order ?

40. Regular Pentagon
A regular pentagon has rotational symmetry of order ? 5
5
4 1
3 2

41. Regular Hexagon
A regular hexagon has rotational symmetry of order ?
Hexagon

42. Regular Hexagon
A regular hexagon has rotational symmetry of order ?

43. Regular Hexagon
A regular hexagon has rotational symmetry of order ? 6
5 6
4 1
3 2

44. Rectangle
A rectangle has rotational symmetry of order ?
Rectangle

45. Rectangle
A rectangle has rotational symmetry of order ? 2
2
1

46. Parallelogram
A parallelogram has rotational symmetry of order ?
Parallelogram

47. Parallelogram
A parallelogram has rotational symmetry of order ? 2
2
1

48. Isosceles Triangle
An isosceles triangle has rotational symmetry of order ?

49. Isosceles Triangle
An isosceles triangle has rotational symmetry of order ? 1
1

50. Scalene Triangle
An scalene triangle has rotational symmetry of order ?
Scalene

51. Scalene Triangle
An scalene triangle has rotational symmetry of order ? 1
1

52. Isosceles Trapezium
An isosceles trapezium has rotational symmetry of order ?
Isos Trapezium

53. Isosceles Trapezium
An isosceles trapezium has rotational symmetry of order ? 1
1

54. Trapezium
A trapezium has rotational symmetry of order ?
Trapezium

55. Trapezium
A trapezium has rotational symmetry of order ? 1
1

56. Kite
A kite has rotational symmetry of order ?
Kite

57. Kite
A kite has rotational symmetry of order ? 1
1
Kite

58. Rotational Symmetry
State the order of rotational symmetry for each shape below:
1 2 3 4
Order 6 Order 2 Order 3 Order 2
5 6 7 8
Order 1 Order 3 Order 2 Order 5
9 10 11 12
Order 4 Order 1 Order 6 Order 8

59. Angle of rotation/order of
rotation
 Square 90 degree 4
 Rectangle 180 degree 2
 Equilateral 120 degree 3
 Circle nil/no limit nil

60. Reflection
(flip)
The result of a figure
flipped over a line.

61. Click on this
trapezoid to
see
reflection.
The result of a figure flipped over a line.

62. Which shapes show reflection,
translation, or rotation?

63. Translation
(Slide)
The action of sliding a
figure in any direction.

64. Click the Octagon
to see
Translation.
The act of sliding a figure in
any direction.

65. HOPE YOU ALL
ENJOYED.
THANKS