Aim: How do we find the area of a circle?

Circle area conjecture: The area of a circle is given by the formula, Area = πr² , where A is the area, r is the radius of the circle.

       Example:

 

Aim:How do we find the area of regular polygons?
March 19, 2012


The area of a regular polygon:
   You can divide a regular polygon into congruent isosceles triangles by drawing segments to each vertex.

Base: S (side)        Altitude: A (apothem)

The variable A appears in the formula for regular polygons. It stands for the length called the apothem, the perpendicular segment from the center to the side of the polygon.


Regular polygon area conjecture:
    The area of a regular polygon is given by the formula 1/2nas, where A is the area, a is the apothem, n is the number of sides ans S is the length.

                   formula: 1/2nas or p= 1/2Pa

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

Area of parallelograms: 
       Area=base x height
                       

Area of trapezoids:
        Area=1/2 x height (b1 + b2)


                                      




















Area of kite: 2 pairs of consecutive congruent sides.
               Area= d1 + d2/2

                                        

Aim:How do we calculate the area of rectangles and triangles?
March 12, 2012


The area of a plane figure is the measure of the region enclosed by the figure. You measure the area of a figure by counting the number of tiles inside.

triangles:
triangle area conjecture - the area of  the 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.

rectangles:

How to find the area of a rectangle:

• The area of a rectangle can be found by multiplying the base times the height.
• If a rectangle has a base of length 6 inches and a height of 4 inches, its area is 6*4=24 square inches

Aim: How do we find compound loci?
March 07, 2012

 compound locus- problem involves two, or possibly more, locus conditions occurring at the same time.  The different conditions in a compound locus problem are generally separated by the word "AND" or the words "AND ALSO".




5 rules of locus:

• 1 point - circle 
• 2 points - 1 line
• 1 line - 2 lines
• 2 lines - 1 line
• two intersecting lines - two intersecting lines 

Aim: 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.

The locus of points equidistant from a single point is a set of points, equidistant from the point in every direction

The locus of points equidistant from two points is the perpendicular bisector of the line segment connecting the two points

The locus of points equidistant from a line are two lines, on opposite sides, equidistant and parallel to that line

The locus of points equidistant from two parallel lines is another line, half-way between both lines, and parallel to each of them

                       The locus of points at a fixed distance, d, from point P is a circle with the given point P as its center and d as its radius.

Aim: What is a mathematical statement?


A mathematical statement is a statement that can be judged true or false.
and:both statements must be true for the statement to be true completely.

There are 4 conditionals:
1.the conditional
2.the inverse
3.the converse
4.contrapositive

Aim:What is logic?


LOGIC is THINKING!!!


Logic is the tool to determine between true or false.
*Inductive reasoning- when your not sure what comes after.

You use logic everyday to...
solve geometry problems
crossing the street 
and moreee!