what are altitudes and angle bisector?

Altitudes are the height of a triangle that meets the ground at a right angle. A angle bisector is when it bisects on a angle in half creating two congruent angles.

what are properties of medians and centroids?

Medians are the line segment a vertex of a triangle to the midpoint of the opposite side. A centroids is the intersection of the three medians in a triangle .

how do we find the volume of cones and pyraminds ?

Cones and pyramids are  A 3-dimensional solid in which the base is a polygon and the sides are triangles which meet in one point called the vertex. A 3-dimensional solid in which the   base is a circle. The side of a cone is formed by straight lines which connect the circular  base  to a vertex. The height is the perpendicular distance from the vertex to the base and meets the  base  in the center of the circle. To find the volume of the pyramids and for cones you need to use the formula of 

 (1/3) b h . 

How do you find the surface area and volume of a sphere ?

A sphere is the set of all points in space equidistant from a given point called a center. To find the surface area you need the formula where S.A=4πr². For the volume you needto use the formula which is 4/3π

 r^{3. This is how you find the surface area and the volume of a sphere.} 

how do we calculate the surface area of a cylinder ?

*We calculate the surface area of a cylinder by L.A+2(B)  .By l which is the length , A is the area and B are the base from the cylinder. That is how we calculate the surface area from a cylinder.

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

*We find the surface area of a pyramid and cones by1/2p.l+ the area of the base. We also find the lateral area of cones and pyramids by 1/2 p.l.

How do we find the area of a regular polygon?

*We find the are of a regular polygon by the formula 1/2nas or 1/2 P.A , where A is the area and P is the perimeter , a is the apothegm , s is the length  of each side, and n is the number of sides. In other words the Area=nas/2 

for example
 - the number of sides are 5
-the apothegm is 2 cm
- and the the length is 8 cm

 so in this case we multiply 5*8*2 =  8 and the we divided it by 2
which give us 40cm² 

How do we find the area of a circle?

*We find the area of a circle by the formula A is the area and R  is the radius of the circle.
In other words . r<sup>2




for example</sup> 
  lets say that r= 8cm 

-in that case since we trying to find the area of the circle we going to use the formula of  a circle which is . r^{2
-we going to substitute r for 8 
-which our formula now is} . 8^{2
-now it equals 64}.

 

How do we find the area of parallelogram,kites and trapezoid ?

*We  find the area of a parallelogram by multiplying the bh. We also find the area of a kite by D1,D2 divided by 2. Lastly, we find the area of a trapezoid by adding both bases and then dividing it by 2. This is how we find the area of a parallelogram , kites and a trapezoid.

How do we calculate the area of rectangles & triangles?

* We calculate the area of a rectangles by multiplying length times width.
* Triangle area conjecture means that the area of a triangle is given by the formula, A=1/2bh. Where A is the area, b is the length of the base and h is the height of the triangle.

how do we find the locus of points?

*The locus is the set of all points that satisfy a given condition.
- A locus is a general graph of a given equation.

- one point:the locus of points equidistant from a single point is a set of points equidistant from the point in every direction.
-two points: (a line through the middle of the two points). the locus  of points equidistant from 2 points is the perpendicular bisector of the line segment connecting the two points
- one line: (two parallel lines on opposite sides , equidistant and parallel to that line.
-Two parallel lines: (a line through the middle of the two line). The locus of points equidistant from 2 parallel line  is another line, half way between both line and parallel to each of them . 

what is a mathematical statement ?

*A mathematical statement is a statement that can be judge to be true or false. In the logic unit we are not just going to look at one statement at a time. We are going to be looking at what happens with multiple statements.

How do we solve logic problems using conditionals ?

 *We can solve conditionals problems by Conditional, Inverse,Converse, Contraoppositive.

 *conditional: you first put the hypothesis and then the conclusion . You also use  "if" at the beginning and
"then" at the end
*Inverse: it whens you switch the you add not to both conclusion and hypothesis
*converse: is just switching the hypothesis and the conclusion
*Contraoppositive.
contra-is a prefix meaning "against" or "opposite"
-so you just negate & switch the hypothesis and the conclusion (inverse and converse) together. 

what is logic?

*Logic is thinking, It is also the tool to determine between true or false .

For example
*3+2= 5      , in this case it is true because 3+2 will equal 5

how do we the other definitions of transformations?

We use the other definitions of transformation by glide reflection,orientation, isometric , and invariant .

*glide reflection: is the reflection of a cine and a translation along the line.

*orientation: refers to the arrangement  of points relative to one another, after a transforming has occured.

*isometric: is a transformation of the plane that preserves length .

*invariant: a figure or property that remains unchanged under a transformation of the plane is referred to as a "invariant" no "variations" have occurred.

how do we graph rotation?

We graph rotation by 90 degrees , 180 degrees and 270 degrees.

*In 90 degrees
 (a-b)----> (-b,a)
  ex.(2,5)--->(-5,2)

*In 180degrees
   (a-b)--->(-a,-b)
   ex.(5,2)--->(-5,-2)

*In 270 degrees
   (a,b)----> (b,-a)
   ex.(2,5)--->(5,-2)

How do we graph dilations?

*Dilations are a type of transformation that causes an image to stretch or shrink in proportion to its original size.
*scale factor
-the ration by which is known as the scale actor



*For example
 (4, 10) (2, 5) the dilation in this is shrink so is D1/2
 (4, 11) (8, 22) in this case the dilation in stretching so is D2

how do we identify transformations ?

We could  indetify trasnformation by translation, reflection,rotation and dilation.

*Translation: every poiny is moved the same distance in the same direction.
*Refletion:figure is flipped over a line of symmetry
*Rotation:figure is turned around a single point.
*Dilation: an anlargement or reduction in a size of an image