Rotational Symmetry 3-2A What is rotational symmetry? How do you identify a figure that has rotational symmetry?

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Presentation transcript:

Rotational Symmetry 3-2A What is rotational symmetry? How do you identify a figure that has rotational symmetry?

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

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. Q P (Pre-image) P’ (Image)Center of rotation Angle of rotation45°

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, Q P (Pre-image) P’ (Image)Center of rotation Angle of rotation45°

Rotating Triangles Rotate triangle RST 90° about point C. R S T C Z Y X 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

Spin It 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.

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.

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.

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.

Assignment 3-2A p. 182, 1-15