Homework Discussion Read pages 372 – 382 Page 394: 1 – 6, 11 – 12,

Translations (page 380) Translations are proper rigid motions. translation - A translation is a slide of an object in the plane. A vector showing the translation can be represented by an arrow giving its direction and length.

A B C

A B C A’ B’ C’

Glide Reflections (page 381) A glide reflection is an improper rigid motion. glide reflection - A glide reflection is a rigid motion consisting of a translation followed by a reflection. The axis of reflection must be parallel to the direction of translation.

A B C

A B C A* B* C* A’ B’ C’

A B C

A B C A* B* C* A’ B’ C’

symmetry - A symmetry of an object or shape is a rigid motion that moves the object back onto itself. identity - The identity motion is itself a symmetry, one possessed by every object and we will simply call it the identity. Symmetry (page 383)

FIGURE The Symmetries of a Square Every square has 8 symmetries - 4 reflection symmetries and 4 rotation symmetries.

FIGURE Two objects or shapes are of the same symmetry type if they have exactly the same set of symmetries. stands for the symmetry type with N reflections and N rotations.

FIGURE Symmetry type

FIGURE 11-20

FIGURE 11-21

FIGURE Symmetry type (only one reflection).

FIGURE This propeller has no reflection symmetries at all! It still has 4 rotation symmetries (identity, and, 90, 180, and 270 degrees). It belongs to the symmetry family called (having 4 rotations only).

FIGURE This propeller has no reflection symmetries. It has 2 rotation symmetries (identity and 180 degrees). It belongs to the symmetry family called (having 2 rotations only).

FIGURE Symmetry type S Z

FIGURE Symmetry type (only identity symmetry).

FIGURE 11-22

Homework Read pages 383 – 388 Page 394: 7, 21 – 24, 27 – 29, 35-45, 47,