What is similar about the shapes in each row? 1. AHOTW 2. CEHO 3. HINO Z

What is similar about the shapes in each row? 1. AHOTW 2. CEHO 3. HINO Z

An object’s symmetry is somehow related to the fact that we can move the object in such a way that when all the moving is done, the object sits exactly as it did before.

Rigid Motions (page 374) rigid motion - The act of taking an object and moving it from some starting position to some ending position without altering its shape or size. equivalent rigid motions - Two rigid motions accomplish the same net effect. image - A rigid motion moves each point in the plane from its starting position P to an ending position P’. We call P’ the image of P under the rigid motion.

Reflections (page 375) reflection - A reflection of the plane is a rigid motion that moves an object into a new position that is the mirror image of the starting position. In two dimensions the mirror is a line, called the axis of the reflection. xx

FIGURE 11-5 Reflections are improper rigid motions. improper rigid motion - We say a reflection is an improper rigid motion to indicate that it reverses the left-right and clockwise-counter clockwise orientations.

A B C A B C A B C A B C

A B C A B C A B C A B C A’ B’ C’ A’ B’ C’ A’ B’ C’ A’ B’ C’

p p’

p

Rotations (page 377) Rotations are proper rigid motions. rotation - For two-dimensional figures, a rotation is described by specifying a point called the center of the rotation (or rotocenter), and an angle indicating the amount of rotation. proper rigid motion - Any rigid motion that always leaves the original orientations (left,right,clockwise, counterclockwise) unchanged is called a proper rigid motion. identity motion - We will agree that not moving an object at all is itself a very special kind of rigid motion of the object, which we will call the identity motion.

0°0° 90° 180° 270° 360° A B

p p’ q q’

p p’ q q’

Homework Read pages 372 – 382 Page 394: 1 – 8, 11 – 12, 16 – 17, 21 – 24,