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Geometry

Geometry. Lesson 7.6 Extended Application: Frieze Patterns. Classifying Frieze Patterns. A frieze pattern or border pattern is a pattern that extends infinitely to the left and right in such a way that the pattern can be mapped onto itself by a horizontal translation

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Geometry

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  1. Geometry Lesson 7.6 Extended Application: Frieze Patterns

  2. Classifying Frieze Patterns • A frieze pattern or border pattern is a pattern that extends infinitely to the left and right in such a way that the pattern can be mapped onto itself by a horizontal translation • Some frieze patterns can be mapped onto themselves by other transformations: • Translation (T) • A 180° rotation (R) • A reflection about a horizontal line (H) • A reflection about a vertical line (V) • A horizontal glide reflection (G)

  3. Examples of Frieze Patterns • Name the transformation that results in the frieze pattern

  4. Name the transformation that results in the frieze pattern Horizontal Translation Horizontal Translation Or 180° Rotation Horizontal Translation Or Reflection about a vertical line Horizontal Translation Or Horizontal glide reflection

  5. Frieze Patterns in Real-Life

  6. 7 Categories of Frieze Patterns

  7. Classifying Frieze PatternsUsing a Tree Diagram

  8. Classifying Frieze Patterns • What kind of frieze pattern is represented?

  9. Classifying Frieze Patterns • What kind of frieze pattern is represented? • TRHVG • It can be mapped onto itself by a translation, a 180° rotation, a reflection about a horizontal or vertical line, or a glide reflection

  10. Classifying a Frieze Pattern A portion of the frieze pattern on the above building is shown. Classify the frieze pattern. TRHVG

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