9 6 Compositions of Reflections Essential Questions How

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9. 6 Compositions of Reflections Essential Questions: How do you use a composition of

9. 6 Compositions of Reflections Essential Questions: How do you use a composition of reflections? How do identify glide reflections?

• Theorem 9 -1 – A translation or rotation is a composition of

• 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.

Example 2

Example 2

Example 3

Example 3

Practice • Find the image of each letter through a reflection across line L

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

• Fundamental Theorem of Isometries – In a plane, one of two congruent

• 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.

Example 4

Example 4

What transformation is missing? • Theorem 9 -5 – Isometry Classification Theorem • There

What transformation is missing? • Theorem 9 -5 – Isometry Classification Theorem • There are only four isometries. They are the following:

Example 5

Example 5

Summary • Answer the essential questions in detailed, complete sentences. • How do you

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.