Line Segment

Parallel Lines

Parallel lines

never intersect!

Parallel lines can go on forever, or they can stop.

Perpendicular lines always have to have a

right angle

.

Perpendicular lines also

always intersect.

Lines

Composition of Transformations

A composition of transformations is the

result

of performing/ putting more than one composition.

The symbol is an open circle.

You must do it in order, and you read it left to right.

Glide Reflections

A glide rotation is a

translation

and a

reflection

that is preformed one after another.

Glide reflections are

commutative

because the line of reflection is parallel to the direction of the transformation.

Reflections

Re

fl

ections - Flip

Reflections are also isometries.

The rules for reflections are-

Reflect over x-axis- (x,y) (x,-y)

Reflect over y-axis- (x,y) (-x,y)

Reflect over y=x- (x,y) (y,x)

Reflect over y=-x- (x,y) (-y,-x)

Reflect over origin- (x,y) (-x.-y)

Rotations

**MATH**

With Fredrick the Fish

With Fredrick the Fish

Translation

Tran

sl

ation- Slide

Translations are isometries.

Translations can be written in three ways, Ex.

To the left 2 units and up 4 units.

Prime Notation- (x,y) (x-2,y+4)

Vector Notation- (x,y) <-2,4>

Rota

t

ions- turn

Rotations are also isometies.

The rules for rotations-

90 degrees - (x,y) (-y,x)

180 degrees- (x,y) (-x,-y)

270 degrees- (x,y) (y,-x)

Dilations

Dilation- Little/Large

Dilations are NOT isometries!!!

Dilations have

scale factors

- Scale Factors are the ratios to make the

pre-image

larger or smaller.

The dialation formula is (x,y) (kx,ky). K is the scale factor.

Perpendicular Lines

A line segment has

2 end points

.

A line segment also

does not go on forever.

Vector notation is written like-

(x,y) <x,y>

Prime Notation is written like-

(x-2, y+4)

Vector and prime notation are ways to write a translation.

Definitions

Angles

There are three kinds of angles-

Obtuse angle

- An angle that is greater then 90 degrees.

Right angle

- An angle that is 90 degrees.

Acute angle

- An angle that is less than 90 degrees.

Plane

A

flat

surface.

Origin

The origin is the (0,0) mark on the graph.

Rotational Symmetry

Rotational Symmetry is when you can rotate a shape and it still looks the same.

Equiangular and Equilateral

Equiangular

is when more than two angles are the same.

Equilateral

is when more than two sides are the same.

Order

Order is numbers arranged sequentially.

example-

1,2,3,4,5,6,7,8,9,10

Bisector

A bisector is a line that passes through a shape evenly.

Congruent

When shapes are exactly the same.

Orientation

Orientation is the way something is positioned.