what properties of medians and centroids ?

medians - the line segment connecting a vertex of a triangle to  the midpoint of the opposite side.

centroids - the intersection of the 3 medians in a triangle (every triangle)

what are angle bisectors , altitudes , perpendiclar bisectors ?

Altitude - the height of a triangle . meets the "ground" at a right angle . (go through vertex)

Bisectors - a line segment  through a vertex perpendicular to a line containing the opposite side .

Angle Bisectors - bisects an angle in half , creating two congruent angels

formulas for volume :]

cylinder = v=Bh
pyramid = v= 1/3Bh
right circular cone =v=1/3Bh
sphere = v = 4/3 . pie . R . cubed

formulas :] for area

rectangles : A=bh

Triangles : A = bh/2

Circles : A= pie  . R . squared 


cylinder = SA = LA + 2B
                 LA= 2pie . R . height 


parallelogram = A=bh 


trapezoid = 




polygons = A = nas/2

kite = d1d2/2

prism = SA = LA+2B
             LA= PH

Pyramid = SA =LA+B
                 LA=pl/2


                         
                        

how do we find the surface area of cones ?

the base of a cone is a circle and the other end (vertex) is pointed similar to a pyramid .
slant height of a cone is the distance from the vertex of a point on the edge of a base
 formulas _

lateral area =  RL

surface area = LxA+ base 

how do we find the surface area and lateral area of pyramids and cones ?

 pyramids - a solid that connects a polygon base to a point

slant height - pyramid is the height of one of the lateral faces .

Formula surface area -
SA=1/2 PL + base area

formula lateral area -
LA= 1/2 PL

how do we calculate the area of rectangles and triangles ?

to find the area of a rectangle is simple just do base x height .

to find the area of a triangle we would need to do the formula -
A=1/2 bh

How do we find the area of parallelograms , kites , and trapezoids?

Trapezoid -a quadrilateral with a pair of parallel sides .

* but to find the area you simply do -


kite- a 2 pair of consecutive congruent sides
* but to find the area you simply do -



parallelogram - a parallelogram is a foh/ur sided figure with all sides parallel
*but to find the area you can simply do -

 (base x height)
                                                   

how do we find the area of a circle ?

how do we find the area of a regular polygon?

a = apothem
s= side
n= number of sides

formula = N (as/2)

how do we solve the locus of problems ?

loci - a loci is a path that satisfy a certain condition . below are listed fundamental loci theorems :

loci rule number 1 : the locus of points at a fixed distance  is a circle

loci rule number 2 : the locus of points at a fixed distance is a pair of parallel lines on either sides ,  .

loci rule number 3 : the locus of points equidistant from two points ; bisectors of the line segment determined by  two points

loci rule number 4 : the loci of points equidistant from two parallel  lines and there is a parallel line midway between them .

loci rule number 5 : the loci of points equidistant from two intersecting lines , and there are a pair of angle bisectors that bisect the angles

what is logic ?

Throughout this week we learned about logic :
       as normal thinking people we use logic on a daily bases .

but you still may be asking yourself what logic is well if you must know logic is "the system or  principle of reasoning  applicable  to any branch of knowledge or study ".

An example of logic would be crossing the street , that moment of should i cross the street now or later could be considered logic .

What is a Mathematical Statement ?

 * A statement that can be judged to be true or false , open sentences . mathematical statements where there is a "variable ".

  Negations - "not "
Always have the opposite truth value add a "not "

In the logic not , we are not going to look at one statement at a time . we are looking at multiple like :

" the president of the united states is Barack Obama and the vice president is joe biden

and ---> both statements must be true for the statement to be true

i am going to have pizza or tacos for dinner.

Conditional -
          conditional is the most frequently used statement in the construction or in the argument of mathematics .

the conditional -
   If it is raning , then it is cloudy

the converse -
   if it is cloudy , then it is raining

the inverse -
       if its not raining , then it is not cloudy

the contrapositive  -
    if its not cloudy then its not raining

How do we solve compositions of transformation problems ?

composition of transformation - when you have two or more transformations that are combined to form  a new transformation , the result is called a composition of transformation

when solving a composition you will do the second part first then the first part .

How do we use the other definitions of Transformations ?

Glide relfection - the combination of a reflection in a line and a translations along that line .

Orientation - orientation refers to the arrangement of points , relative to one another , after a tranformation  has occurred .

Isommetry - an isommetry is a transformation of the plane that preserves length

Direct isommetry - orientation of the isommetry remains the same .

Opposite isommetry - an isommetry that changes the order such as something going  from clockwise to counter clockwise .

Invareant - a  figure or property that remains unchanged under a transformation of the plane is referred to as invareant . ( no varreation have occurred )

How do we Graph Dilation's ?

Dilation- is a type of translation that causes an image to stretch or shrink in proportion to its original size .

scale size - the rotation by which the image stretches or shrinks is known as the scale factor . If the scale factor is  grater then 1 then  it will be enlarged . if the image scale factor is >0 and <0 then the image will shrink .

NOW YOU ARE READY TO GRAPH DILATION'S !

How do we Graph Rotations ?

Describing Rotations -
1) Angle of rotation
2) a direction (clockwise or counterclockwise )
3) center of rotation
       
when solving for a rotation you may also be able to use a formula ; i prefer the formula :

90 degrees -
(A,B)------->(-B,A)

180 degrees -
(A,B)-------->(-A,-B)

270 degrees -
(A,B)-------->(B,-A)

note :
   Whenever the problem does not state it is clockwise it is automatically counter clockwise , but the the formula will switch the problem for you automatically .

How do we Graph Transformations that are Reflections ?

Reflections - Line of symmetry
       * A figure has a line of symmetry  , if a line can be drawn down the figure so that it divides the figure into a mirror image

Line of reflection -
    (FLIP) a transformation that creates figures which are mirror images .

           x-axis    (x,y)-------------(x,-y)
          y-axis     (x,y)-------------(-x,y)

How do we Identify Transformations

Objective - Identify transformations including transformations such as Rotation , Reflection , and Dialation , and Transformation .

Transformation - When you move a figure .

Translation - Every point is moved the same distance in the same direction

Reflection - A figure flipped over a line of symmetry

Rotation -Figure is turned around a single point .

Dialation - Enlargement or reproduction in size of an image .