Rotational Symmetry 3-2A

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Rotational Symmetry 3-2A

• What is rotational symmetry?
• How do you identify a figure that has rotational
  symmetry?

2
How Many Degrees
180 90 270

• are in a half turn?
• are in a quarter turn?
• three quarters turn?

3
Definition

• A rotation is a transformation that turns a set
  of points about one point, the center of
  rotation. The pre-image and image of any point
  are the same distance from the center of
  rotation.

P (Pre-image)
Angle of rotation
45
Q
P (Image)
Center of rotation
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Definition continued

• The angle of rotation measures how much a point
  is turned about the center. For example, if
  point P is rotated 45 clockwise about center of
  rotation Q,

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Rotating Triangles

• Rotate triangle RST 90 about point C.

R
Z
Label the images of points R,S, and T points X,
Y, and Z .
X
C
Draw CR.
S
T
Use a protractor to draw a 90 clockwise angle.
Make CR CX
Y
Repeat the process to find Y and Z
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Spin It

• When will the image exactly overlap the
  pre-image?
• 30 clockwise
• 60clockwise
• 90clockwise
• 120clockwise

If a figure can be rotated onto itself with an
angle or rotation between 0 and 360 , the
figure has rotational symmetry.
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Try It

• Identify the figure(s) that have rotational
  symmetry and the clockwise angles of rotation
  between 0 and 360 that cause the image and
  pre-image to overlap.

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Definitions

• If a figure can be rotated about some point onto
  itself through a rotation of between 0 and 360,
  then it has rotational symmetry.
• A design with rotational symmetry is a rosette.
• A figure that can be rotated onto itself through
  an angle of 180 has point symmetry.
• A rotation of 180 is also known as a half-turn.

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• What is rotational symmetry?
• If a figure can be rotated onto itself with an
  angle or rotation between 0 and 360 , the
  figure has rotational symmetry.
• How do you identify a figure that has rotational
  symmetry?
• If a figures has rotational symmetry, the
  clockwise angles of rotation between 0 and 360
  will cause the image and pre-image to overlap.

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Assignment 3-2A

• p. 182, 1-15