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

…are in a half turn?
180 °
…are in a quarter turn?
…three quarters turn?
90 °
270 °

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)
Q
Center of rotation
45
°
Angle of rotation
P’ (Image)

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, m

PQP '

45

P (Pre-image)
Q
Center of rotation
45
°
Angle of rotation
P’ (Image)

Rotate triangle RST 90 ° about point C.
Z
Label the images of points R,S, and T points X, Y, and Z .
Draw CR.
Use a protractor to draw a
90 ° clockwise angle. Make
CR = CX
Repeat the process to find
Y and Z
T
Y
C
R
S
X

When will the image exactly overlap the pre-image?
30 ° clockwise
60 °clockwise
90 °clockwise
120 °clockwise
If a figure can be rotated onto itself with an angle or rotation between 0 ° and 360 °, the figure has rotational symmetry
.

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.

• 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 halfturn.

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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