Rotations and Rotational Symmetry

1
Rotations and Rotational Symmetry

• We are learning torotate a figure, describe a
  rotation, and identify rotational symmetries.
• Monday, June 24, 2013

2
Vocabulary

• A rotation turns a figure around a fixed point a
  certain number of degrees either clockwise or
  counterclockwise.
• The new figure is congruent (exactly the same
  shape and size) to the original figure.

3
Degrees in a Circle Review
360
0
22.5
315
45
45
45
90
90
45
45
90
270
45
45
90
90
45
45
135
225
180
4
Estimating Rotations Describe how the
following figures have been rotated around the
point of rotation.
Original Object
Clockwise About 90
Point of Rotation
Rotated Object
Counterclockwise About 270
To find the missing rotation subtract from
360(360 90 ?)
5
Estimating Rotations Describe how the
following figures have been rotated around the
point of rotation.
Original Object
Counterclockwise About 45
Rotated Object
Point of Rotation
Clockwise About 315
90
180
To find the missing rotation subtract from
360(360 45 ?)
6
Estimating Rotations Describe how the
following figures have been rotated around the
point of rotation.
Original Object
Point of Rotation
Counterclockwise About 225
Rotated Object
180
Clockwise About 135
90
To find the missing rotation subtract from
360(360 135 ?)
7
Vocabulary

• A figure has rotational symmetry when it can be
  rotated less than 360 around a central point and
  then fit exactly on top of itself.
• http//www.learner.org/courses/learningmath/geomet
  ry/session7/part_b/index.html

8
Rotational Symmetry

• Order of a Rotational Symmetry The amount of
  times that an object fits on top of itself when
  being rotated.
• Calculating Rotational Symmetries
• Find the Order of the Rotational Symmetry
• Divide 360 by the Order of the Rotational
  Symmetry
• This value represents the first Rotational
  Symmetry.
• Continue adding this value to find the next
  Rotational Symmetry.
• Add this value until you reach 360.

9
Rotational Symmetry Practice
Practice finding Rotational Symmetries with your
team!
Order of Rotational Symmetry
6
1
6
Calculate the Rotational Symmetries
360 6
60
5
2
List all Rotational Symmetries
(60)
(60)
(60)
180,
120,
60,
(60)
(60)
240,
360
3
4
300,