Chapter Twelve:  
Transformations

Geometry   Notes

Chapter  12

Section  12.1
Section  12.2
Section  12.3
Section  12.4
Section  12.5
Section  12.6
Section  12.7

Geometry Contents

 

Take notes on the following topics.

Section 12.4  Compositions of Reflections

Vocabulary

Glide reflection (p. 656) A glide reflection is the composition of a translation followed by a reflection in a line parallel to the translation vector.

Theorem 12-1

A translation or rotation is a composition of two reflections.

Theorem 12-2

A composition of reflections in two parallel lines is a translation.

Theorem 12-3

A composition of reflections in two intersecting lines is a rotation.

Theorem 12-4  Fundamental Theorem of Isometries

In a plane, one of two congruent figures can be mapped onto the other by a composition of at most three reflections.

Theorem 12-5

There are only four isometries. They are reflection, translation, rotation, and glide reflection.