r_x-axis

(x, - y)

x is lazy & doesn't change

r_y-axis

(-x, y)

y is lazy & doesn't change

r_y=x

(y,x)

switch order

r_{y = - x}

(-y, -x)

switch & negate

R_O,90

(- y, x)

R_{O, 180}

(-x, -y)

R_{O, 270}

(y, -x)

T_a,b

(x+a, y+b)

r_origin

(-x,-y)

Golden Rule for Rigid Motion Explanation as to why 2 triangles are congurent

A series of rigid motions (you list the specific ones you did in the problem) MAPS shape 1 onto shape 2. Rigid motions preserve segment length and angle measure, therefore the image is congruent to the pre-image.

Line reflection

is the Perpendicular Bisector of the line segment connecting each pre-image point to its image.

Orientation

The arrangement (or how you name the shape) of the points before and after a transformation.

If it is preserved, the order and direction will be the same in the pre-image and the image.

Orientation NOT is preserved for what type of transformation?

a line reflection

what does the line x = # look like?

a Vertical line

what does the line y = # look like?

a Horizontal line

Rotation notation must have three things: CDD

C: Center of Roation

D: Direction of Rotation ( + = Counter clockwise (CCW) & - = clockwise (CW))

D: Degree of Rotation

EX: R_O,-90

Theta = angle measurement symbol

Regular Polygons

A shape with ALL SIDES CONGRUENT & ALL ANGLES CONGRUENT

Regular Pentagon

5 sides

Regular HeXagon

siX sides

Regular Heptagon

7 sides

Regular Octogon

8 sides

Regular Nonagon

9 sides

Regular Decagon

10 sides

Regular Dodecagon

12 sides

Point Symmetry

If you turn a shape upside down (or R_{O, 180}) and it looks the same, then it has point symmetry

Roational Symmetry

The number of degrees less than 360 it takes to map a shape onto itself.

If your shape is a regular polygon then the formula to find the rotational symmetry is: 360/ n (where n is the number of sides)

Line Symmetery

the "Fold Line" that divides a shape into 2 identical halves

Composition Notation

**Work Backwards**