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Symmetry

A plane figure that can be folded along a line so the two parts match.

reflection

It is a transformation that flips a figure over a line of reflection.

rotation

It is a transformation that turns a figure about a fixed point.

Transformation

a movement on the cartesian plane

Rotational Symmetry

If you can rotate (or turn) a figure around a center point by fewer than 360° and the figure appears unchanged, then the figure has rotation symmetry.

Asymmetrical

Not identical on either side of a central line

Symmetrical

When one half is a mirror image of the other half.

Axis of Symmetry

a line that divides a parabola in two equal halves and goes through the vertex

line of symmetry

The line that divides two matching parts. It can be vertical, horizontal, or diagonal.

translation

It is a transformation that moves points the distance and in the same direction.

line of reflection

The line over which a figure is reflected. The vertices of the original and new figure are the same distance from this. The line of reflection can be the x-axis, the y-axis, or any line on the coordinate plane.

90 rotatipn counter clockwise around the orgin

The coordinates switch and negate the second one

180

(X,Y) to (-X,-Y)

270 clockwise and 90 counterclockwise

Negate the first one (X,Y) to (-X,Y)

Isometry

a transformation that does not change the size or shape of a figure

Rotational symmety

Can be rotated less than 180 degrees around a point that maps the figure onto itself

Point of symmetry

Rotational symmetry of exactly 180 degrees(looks the same upside down)

Dilation

a transformation that changes the size of an object, but not the shape

90

What degree is rotating a quarter turn?

270

What degrees is rotating three quarters turn?

180

What degrees is rotating a half turn?

Change the y coordinates to the opposite (x,y)-(x,-y)

How do you preform a reflection across the x-axis?

How do you preform a reflection across the y-axis?

Change the x coordinates to the opposite (x,y) (-x,y)

Swap the x and y values

How do you preform a reflection across the y=x?

1.label the coordinates

How do you preform a reflection across the y=-x axis?

How do you preform a dilation?

Multiply the coordinates by the scale factor

What does the graph y=x look like?

A line going straight through(0,0) from the bottom left to the top right

What does the y=-x look like?

A line going straight through(0,0) from the top left to the bottom right

Vectors

Direction w/ Quantities

Equal vectors

Two vectors w/ the same length and direction

i

goes 1 unit to the right

j

goes 1 unit up

O Sigma

Refers to a general isometry

fixed point

object that supports the pendulum

Counterclockwise

the figure moves the opposite direction as a clock

Clockwise

the figure moves the same direction as a clock moves

Direct Isometry

No change in orientation

Opposite Isometry

Changes the orientation

Direct

All translations are...

opposite

Two numbers that are an equal distance from zero on a number line; also called additive inverse.

orientation

the direction in which an figure is facing

Identity

The product of any number and one is that number.

reflections UjUl

An isometry that fixes to exactly one point is the product of two...

Every isometry is either the...

identity, a reflection, or the product of 2 or 3 reflections

translation (find V)

The product of rotations with angles that is a multiple of 360 degrees is...

rotation (find C)

The product of rotations with angles that are not multiples of 360 degrees is...

rotation of alpha with a different center

The product of a translation and a rotation of alpha is a...

glide reflection

The product of a translation and a reflection when the vector and line are parallel...

acute triangle

A triangle with three acute angles.

obtuse triangle

A triangle with one obtuse angle.

Right Triangle

A triangle with one right angle.

Scalene Triangle

A triangle with no congruent sides

Isoceles triangle

At least two sides of a triangle are congruent.

equilateral triangle

Triangle with a 90° angle

Parallelogram

p=s+s+b+b

Rectangle

A parallelogram with 4 right angles

Rhombus

a parallelogram with four equal sides and equal opposite angles.

Square

P=s+s+s+s

Trapezoid

P=s1+s2+b1+b2

polygon

a closed figure made by joining line segments where each line segment intersects exactly 2 others

regular polygon

a convex polygon in which all sides and angles are congruent

triangle

P=a+b+c

Quadrilateral

A polygon with 4 sides and 4 angles.

pentagon

a 5 sided polygon

hexagon

a 6-sided polygon

Septagon

A 7-sided polygon

octagon

an 8-sided polygon

nonagon

a 9-sided polygon

decagon

a 10-sided polygon