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Lesson Plans and Worksheets for Grade 8

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Common Core For Grade 8

### New York State Common Core Math Grade 8, Module 2, Lesson 9

Worksheets and solutions for Common Core Grade 8, Module 2, Lesson 9

### Lesson 9 Student Outcomes

• Students learn that sequences of rotations preserve lengths of segments as well as degrees of measures of angles.

• Students describe a sequence of rigid motions that would map a triangle back to its original position after being rotated around two different centers.

Lesson 9 Summary

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

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

• 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.

Classwork

Exploratory Challenge

1.

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?

2.

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.

3.

a. Rotate △ ABC 90°(counterclockwise) around center D then rotate the image another 90°(counterclockwise around center E. Label the image △ A'B'C'.

a. Rotate △ ABC 90°(counterclockwise) around center E 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 figures image?

4.

a. Rotate △ ABC 90°(counterclockwise) around center D then rotate the image another 45°(counterclockwise) around center D. Label the image △ A'B'C'.

b. Rotate △ ABC 45°(counterclockwise) around center D 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 figures image?

5. △ 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'.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Lesson Plans and Worksheets for Grade 8

Lesson Plans and Worksheets for all Grades

More Math Lessons for Grade 8

Common Core For Grade 8

Examples, videos, and solutions to help Grade 8 students learn that sequences of rotations preserve lengths of segments as well as degrees of measures of angles.

• Students learn that sequences of rotations preserve lengths of segments as well as degrees of measures of angles.

• Students describe a sequence of rigid motions that would map a triangle back to its original position after being rotated around two different centers.

Lesson 9 Summary

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

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

• 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.

Classwork

Exploratory Challenge

1.

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?

2.

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.

3.

a. Rotate △ ABC 90°(counterclockwise) around center D then rotate the image another 90°(counterclockwise around center E. Label the image △ A'B'C'.

a. Rotate △ ABC 90°(counterclockwise) around center E 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 figures image?

a. Rotate △ ABC 90°(counterclockwise) around center D then rotate the image another 45°(counterclockwise) around center D. Label the image △ A'B'C'.

b. Rotate △ ABC 45°(counterclockwise) around center D 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 figures image?

5. △ 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'.

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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