what is similar about the shapes in each row? 1. ahotw 2. ceho 3. hino z
Post on 23-Jan-2016
223 views
TRANSCRIPT
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