lesson 9: sequencing rotations - ms....

Lesson 9: Sequencing Rotations Date: 9/18/13

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NYS COMMON CORE MATHEMATICS CURRICULUM 8ͻϮ Lesson 9

Lesson 9: Sequencing Rotations

Classwork Exploratory Challenge

1.

a. Rotate ᇞ Label the rotated image as ᇞ .ܦ d degrees around center ܥܤܣ .ԢܥԢܤԢܣb. Rotate ᇞ Label the rotated image as ᇞ .ܧ Ԣ d degrees around centerܥԢܤԢܣ .ԢԢܥԢԢܤԢԢܣc. Measure and label the angles and side lengths of ᇞ How do they compare with the images ᇞ .ܥܤܣ Ԣ andܥԢܤԢܣ

ᇞ ?ԢԢܥԢԢܤԢԢܣ

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?

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2.

a. Rotate ᇞ Label the image .ܧ and then rotate again degrees around center ܦ d degrees around center ܥܤܣas ᇞ .Ԣ after you have completed both rotationsܥԢܤԢܣ

b. Can a single rotation around center ܦ map ᇞ Ԣ onto ᇞܥԢܤԢܣ ?ܥܤܣ

c. Can a single rotation around center ܧ map ᇞ Ԣ onto ᇞܥԢܤԢܣ ?ܥܤܣ

d. Can you find a center that would map ᇞ Ԣ onto ᇞܥԢܤԢܣ .ܨ in one rotation? If so, label the center ܥܤܣ





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3.

a. Rotate ᇞ ƚŚĞŶƌŽƚĂƚĞƚŚĞŝŵĂŐĞĂŶŽƚŚĞƌϵϬȗ;ĐŽƵŶƚĞƌĐůŽĐŬǁŝƐĞ ܦ ͻͲǏ (counterclockwise) around center ܥܤܣaround center ܧ. Label the image ᇞ .ᇱܥᇱܤᇱܣ

b. Rotate ᇞ ƚŚĞŶƌŽƚĂƚĞƚŚĞŝŵĂŐĞĂŶŽƚŚĞƌϵϬȗ;ĐŽƵŶƚĞƌĐůŽĐŬǁŝƐĞ ܧ ͻͲǏ (counterclockwise) around center ܥܤܣaround center ܦ. Label the image ᇞ .ԢԢܥԢԢܤԢԢܣ

c. What do you notice about the locations of ᇞ Ԣ and ᇞܥԢܤԢܣ ԢԢ? Does the order in which you rotate aܥԢԢܤԢԢܣfigure around different centers have an impact on the final location of the figures image?





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4.

a. Rotate ᇞ ͻͲǏ (counterclockwise) around center D then rotate the image another ͶͷǏ (counterclockwise) ܥܤܣaround center D. Label theᇞ .ᇱܥᇱܤᇱܣ

b. Rotate ᇞ ͶͷǏ (counterclockwise) around center D then rotate the image another ͻͲǏ (counterclockwise) ܥܤܣaround center D. Label theᇞ .ԢԢܥԢԢܤԢԢܣ

c. What do you notice about the locations of ᇞ Ԣ and ᇞܥԢܤԢܣ ԢԢ? Does the order in which you rotate aܥԢԢܤԢԢܣfigure around the same center have an impact on the final location of the figures image?





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5. In the figure below, ᇞ has been rotated around two different centers and its image is ᇞ ܥܤܣ ᇱ. Describe aܥᇱܤᇱܣsequence of rigid motions that would map ᇞ onto ᇞ ܥܤܣ .ԢܥԢܤԢܣ





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Problem Set 1. Refer to the figure below.

a. Rotate ܥܤܣס and segment ܧܦ degrees around center ܨ, then degrees around center ܩ. Label the final

location of the images as ܣסԢܤԢܥԢ and D’E’.

b. What is the size of ܥܤܣס and how does it compare to the size of ܣסᇱܤᇱܥᇱ? Explain.

c. What is the length of segment DE and how does it compare to the length of segment ܦԢܧԢ? Explain.

Lesson Summary

Sequences of rotations have the same properties as a single rotation:

x A sequence of rotations preserves degrees of measures of angles.

x A sequence of rotations preserves lengths of segments. The order in which a sequence of rotations around different centers is performed matters with respect to

the final location of the image of the figure that is rotated.

The order in which a sequence of rotations around the same center is performed does not matter. The image of the figure will be in the same location.





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2. Refer to the figure given below.

a. Let ݐݐଵ be a counterclockwise rotation of ͻͲǏ around the center . Let ݐݐଶ be a clockwise rotation of (െ45)Ǐ around the center . Determine the approximate location of ݐݐଵ(ᇞ followed (ܥܤܣby ݐݐଶ. Label the image of triangle ܥܤܣ as ܣԢܤԢܥԢ.

b. Describe the sequence of rigid motions that would map ᇞ onto ᇞ ܥܤܣ .ᇱܥᇱܤᇱܣ

3. Refer to the figure given below. Let be a rotation of (െ90)Ǐ around the center . Let ݐݐଶ be a rotation of (െ45)Ǐ around the same center . Determine the approximate location of ݐݐଵ(οܥܤܣ) followed by .ԢܥԢܤԢܣ as ܥܤܣ Label the image of triangle .(ܥܤܣο)ଶݐݐ




lesson 9: sequencing rotations - ms....

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