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Compositions of Isometries

Compositions of Isometries. Essential Understanding. You can express all isometries as a composition of reflections Objectives Students will be able to find compositions of isometries , including glide reflections and classify isometries . Iowa Common Core Standards

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Compositions of Isometries

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  1. Compositions of Isometries

  2. Essential Understanding • You can express all isometries as a composition of reflections • Objectives • Students will be able to find compositions of isometries, including glide reflections and classify isometries. • Iowa Common Core Standards • G.CO.2 - Represent transformations in the plane, describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not • G.CO.5 - Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, graph paper. Specify a sequence of transformations that will carry a given figure onto another • G.CO.6 - Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent

  3. Isometry • Transformation that preserves distance or length • Translations • Reflections • Rotations • The composition of two or more isometries is an isometry

  4. Four Kinds of Isometries

  5. Examples on Sketchpad • Reflections over parallel lines • Reflections over intersecting lines • Glide Reflections

  6. Glide Reflection • Composition of a translation and a reflection across a line parallel to the direction of translation

  7. Homework • Pg. 574 • #6 – 36 (3s) • 11 problems

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