Lesson 7.6 Lesson 7.6 Extended Application: Frieze Patterns

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Presentation transcript:

Lesson 7.6 Lesson 7.6 Extended Application: Frieze Patterns Geometry Lesson 7.6 Extended Application: Frieze Patterns

Objectives/Assignment Use transformations to classify frieze patterns Use frieze patterns to create decorative borders Assignment: 2-34 even

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)

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

Horizontal Translation 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

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7 Categories of Frieze Patterns

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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

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