9.6 Compositions of Reflections

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9.6 Compositions of Reflections

• Essential Questions
• How do you use a composition of reflections?
• How do identify glide reflections?

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• Theorem 9-1
• A translation or rotation is a composition of two
  reflections.
• Theorem 9-2
• A composition of reflections across two parallel
  lines is a translation.
• Theorem 9-3
• A composition of reflections across two
  intersecting lines is a rotation.

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Example 2
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Example 3
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Practice

• Find the image of each letter through a
  reflection across line L and then a reflection
  across line M. Describe the resulting translation.

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• Fundamental Theorem of Isometries
• In a plane, one of two congruent figures can be
  mapped onto the others by a composition of at
  most three reflections.
• A glide reflection is the composition of a glide
  (translation) and a reflection across a line
  parallel to the direction of translation.

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Example 4
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What transformation is missing?

• Theorem 9-5
• Isometry Classification Theorem
• There are only four isometries. They are the
  following

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Example 5
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Summary

• Answer the essential questions in detailed,
  complete sentences.
• How do you use a composition of reflections?
• How do identify glide reflections?
• Write 2-4 study questions in the left column to
  correspond with the notes.