1. 9.5 : Symmetry
I can identify line and rotational symmetries in two‐dimensional figures.
I can identify plane and axis symmetries in three‐dimensional figures.

2. If the images to the right describe symmetry, in your own words, define symmetry:

3. Vocabulary!
Symmetry
 a figure has symmetry if a reflection, translation, rotation, or glide reflection maps a figure onto itself
Line Symmetry
 also called reflection symmetry
the figure can be mapped onto itself by a
reflection in the line
Line of Symmetry
 the line used to map a figure onto itself

4. Example 1:
State whether the object appears to have line symmetry. Write yes or no. If so, draw all lines of symmetry, and state their number.
Yes, 4
Yes, 1
Yes, 4

5. Vocabulary!
Rotational Symmetry
 the figure can be mapped onto itself by a rotation between 0° and 360° about the center of the figure
Center of Symmetry
 the center of the figure used as the fixed point for the rotation

6. Vocabulary!
Order of Symmetry
 the number of times a figure maps onto itself as it rotates from 0° to 360°
Magnitude of Symmetry
 the smallest angle through which a figure can be rotated so that it maps onto itself
magnitude = 360 ÷ order   

7. Example 2:
State whether the figure has rotational symmetry. Write yes or no. If so, locate the center of symmetry, and state the order and magnitude of symmetry.
Yes
Order = 5
Magnitude = (360/5)= 72°
Yes
Order = 3
Magnitude = (360/3)= 120°
Yes
Order = 8
Magnitude = (360/8)= 45°

8. Do the you tries on your own!

9. You Try!
State whether the figure has rotational symmetry. Write yes or no. If so, locate the center of symmetry, and state the order and magnitude of symmetry.

10. You Try!
State whether the figure has rotational symmetry. Write yes or no. If so, locate the center of symmetry, and state the order and magnitude of symmetry.

11. Example 3:
Determine whether the entire word has line symmetry and whether it has rotational symmetry. Identify all lines of symmetry and angles of rotation that map the entire word onto itself.
Rotational 180°
Rotational 180°

12. Three Dimensional Symmetries
Plane Symmetry
Axis Symmetry
 The figure can be mapped onto itself by a reflection in the plane
the figure can be mapped onto itself by a rotation between 0° and 360° in a line

13. Example 4:
State whether the figure has plane symmetry, axis symmetry, both, or neither.
a) b)
Both
Neither

14. Do the you tries on your own!

15. You Try!
State whether the figure has plane symmetry, axis symmetry, both, or neither. 1.

16. You Try!
State whether the figure has plane symmetry, axis symmetry, both, or neither. 2.

17. You Try!
State whether the figure has plane symmetry, axis symmetry, both, or neither. 3.

18. You Try!
State whether the figure has plane symmetry, axis symmetry, both, or neither. 4.

19. You Try!
State whether the figure has plane symmetry, axis symmetry, both, or neither. 5.

20. You Try!
State whether the figure has plane symmetry, axis symmetry, both, or neither. 6.