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. A H O T W

2. C E H O

3. H I N O Z

What is similar about the shapes in each row?

1. A H O T W

2. C E H O

3. H I N O 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.

x x

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

BCA

B

C

A

B

C

A

B

C

A

BCA

B

C

A’

B’

C’

A’

B’

C’

A’

B’ C’ A’

B’

C’

p

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°

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, 27 - 30