Compositions of Reflections

1
Compositions of Reflections

• 3.4
• Show how reflections are related to other
  iosmetries

2
Theorem

• 3.1 A composition of reflections in two //
  lines is a translation
• 3.2 A composition of reflections in two
  intersecting lines is a rotation
• 3.3 In a plane, two congruent figures can be
  mapped onto one another by a composition of at
  most three reflections
• 3.4 There are only 4 isometries
• 1) reflection 2) translation 3) rotation 4) glide
  reflection

3
Definition

• Glide reflection a composition of three
  reflections in lines that intersect in more than
  one point
• Note be sure to always glide first, then reflect

4
Examples

• Open book to p. 145 and do examples 1-4

5
Paper

• Get some out!
• Draw a P on the paper and another P away from
  the first that is congruent and in a different
  direction
• Lets first use 3 reflections to map P
• Now lets use glide reflection

6
Homework

• Page 148 1-28