Rotational Symmetry
- Author:
- Ashley Hobbs
a. Rotate △ ABC d degrees around center D. Label the rotated image as △ A′B′C′.
b. Rotate △ A′B′C′ d degrees around center E. Label the rotated image as △ A′′B′′C′′.
c. Measure and label the angles and side lengths of △ ABC. How do they compare with the images △ A′B′C′
and △ A′′B′′C′′?
d. How can you explain what you observed in part (c)? What statement can you make about properties of
sequences of rotations as they relate to a single rotation?
a. Rotate △ ABC d degrees around center D, and then rotate again d degrees around center E. Label the image
as △ A′B′C′ after you have completed both rotations.
b. Can a single rotation around center D map △ A′B′C′ onto △ ABC?
c. Can a single rotation around center E map △ A′B′C′ onto △ABC?
d. Can you find a center that would map △A′B′C′ onto △ ABC in one rotation? If so, label the center F.
a. Rotate △ ABC 90° (counterclockwise) around center D, and then rotate the image another 90°
(counterclockwise) around center E. Label the image △ A′B′C′.
b. Rotate △ ABC 90° (counterclockwise) around center E, and then rotate the image another 90°
(counterclockwise) around center D. Label the image △ A′′B′′C′′.
c. What do you notice about the locations of △ A′B′C′ and △ A′′B′′C′′? Does the order in which you rotate a
figure around different centers have an impact on the final location of the figure’s image?
a. Rotate △ ABC 90° (counterclockwise) around center D, and then rotate the image another 45°
(counterclockwise) around center D. Label the image △ A′B′C′.
b. Rotate △ ABC 45° (counterclockwise) around center D, and then rotate the image another 90°
(counterclockwise) around center D. Label the image △ A′′B′′C′′.
c. What do you notice about the locations of △ A′B′C′ and △ A′′B′′C′′? Does the order in which you rotate a
figure around the same center have an impact on the final location of the figure’s image?
△ ABC has been rotated around two different centers, and its image is △A′B′C′. Describe a sequence of rigid motions that would map △ ABC onto △A′B′C′.