Isometries

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Isometries
Page 15-19
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Isometry A transformation in a plane that
results in an image that is congruent to the
original object.

• Which transformations are isometries?
• Line reflections
• Point reflections
• Translations
• Rotations
• Glide Reflection

Dilations are NOT isometries. They do not
preserve distance!!
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Direct Isometry An isometry that preserves
orientation.

• Which transformation are direct isometries?
• Point reflections
• Translations
• Rotations

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Point reflection in the origin.
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Translation
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Rotation
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Opposite Isometry An isometry that does not
preserve orientation.

• Which transformation are opposite isometries?
• Line reflections
• Glide reflections

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Glide Reflection
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Compositions with Isometries
An even number of opposite isometries results
in a direct isometry
An odd number of opposite isometries results in
an opposite isometry
Direct isometry
D
D
Opposite isometry
O
D
Opposite isometry
D
D
O
D
Direct isometry
O
D
O
D
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