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Unformatted text preview: on the circle C( P, PX ) such that ∠ XPX' ≅ ∠ ABC = θ . θ . ∠ WPW' ≅ ∠ XPX' ≅ ∠ YPY' ≅ ∠ ZPZ' ≅ ∠ ABC = θ The Four Isometry Types III. Rotations R P , θ Given directed angle θ = ∠ ABC and point P: Inverse: ( R P , θ )1 = ( R P ,  θ ) = ( R P , 360 ° θ ) The Rotation about point P through directed angle θ = ∠ ABC is R P , θ . Z ' Y ' W' X ' B C A X W Y Z P K ' Mirror line m C' = T AB ( Z ) Given a mirror line m and a vector AB which is parallel to m : The Four Isometry Types IV. Glide Reflections GL AB , m Z = R m ( C ) Inverse: ( GL AB , m )1 = R m ° T BA Thus, for any point X, X' = GL AB , m (X) = T AB ( R m (X) ) = R m ( T AB (X) ) The Glide Reflection about mirror line m through vector AB (parallel to the mirror line) is GL AB , m , where GL AB , m = T AB ° R m . Also, GL AB , m = R m ° T AB . M J ' H ' G ' F ' E ' D ' C ' L' Z A L C D E F G H J K B...
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 Spring '10
 Shirley
 Vectors, Line segment, Elementary geometry, glide reflection, L F K D C M J

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