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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