 Complete the Summary of Transformations handout. Translation of h units horizontally and y units vertically Reflection over the y-axis Reflection over the x-axis Reflection over the line y = x Rotation of 90 clockwise about the origin Rotation of 180 Rotation of 90˚ counterclockwise about the origin

Lesson 9-4

 An isometry is a transformation that preserves distance or length.  Translations  Reflections  Rotations  These are all isometries because the distances/lengths are preserved.  A fourth isometry is called a glide reflection.

 Remember that a composition of transformations is a combination of two more transformations.  Complete the investigations:  Reflections across parallel lines  Reflections across intersecting lines

 The composition of reflections across parallel lines results in what type of transformation?  translation  What is the distance that the figure is translated?  Twice the distance between the parallel lines  The composition of reflections across intersecting lines results in what type of transformation?  rotation  What is the angle of rotation?  Twice the angle formed by the intersecting lines.

 Compositions of Transformations Worksheet

 Entry Task: What are the four types of isometries?  Theorem:  The composition of two or more isometries is an isometry.  Any composition of isometries can be represented by either a reflection, translation, rotation, or glide reflection.  A glide reflection is a composition of a translation (glide) and a reflection across a line parallel to the direction of the translation.

 Page 574 (6-22 evens, all, evens)  Read Lesson 9-6 on pages