Math Chapter 1 and 2
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Inductive reasoning
method used for drawing conclusions from a limited set of observations. General> Specific

deductive reasoning
logic to draw conclusions from statements already accepted as true.

point
 zero dimensions
 has locations only
 capital letter (A,B,C)

line
 straight path with no thickness (one dimension)
 infinite number of points
 extended without end in both directions

line segment
part of a line thats bounded by two end points

plane
 flat unbounded (infinite) surface with no thickness
 two dimensional
 represented by a parallelogram
 capital letter in corner

colinear
points contained by the same line

coplaner
points that contained in the same plane

noncollinear
points not on a single line

concurrent
lines that contain a common point

ray
 part of a line that extends endlessly in one direction
 name using endpoints first
 symbol points to the right

angle
 a pair of rays that share the same endpoint
 sides: rays
 vertex common endpoint
 name using 3 points

polygon
 lies in a plane
 bounded by line segments
 two dimensional

polyhedron
 lies in space
 bounded by polygons (no curves)
 three dimensional

perimeter
 sume of the lengths of its sides
 measured in units

area
surface included in square units or units^{2}

circle
set of all points that are a fixed distance or radius from a given point in the plane.

constructions
created with straightedge and compass

bisect
to divide into two equal parts

quadrilateral formula
A= 1/4(a+c)(b+d)

conditional statements
consists of two clauses, one which begins with the word "if" or "when" or some equivalent word

hypothesis
the letter a or "if"

conclusion
the letter b or "then"

Euler diagram
uses circles to illustrate how conditional statements relate to each other

converse
statement found by interchanging the hypothesis and conclusion of the conditional statement

contrapositive
statement formed by interchanging the a and b and denying both

inverse
formed by denying both a and b

syllogism
 an argument in the from
 a> b
 b> c
 a>c

Direct Proof
argument of syllogism

premises
statements of the arguement

conclusion
conncets the first to the last

theorem
statement that is proved by reasoning deductively from already accepted statements

Indirect proof
assumption made at the beginning that leads to a contradiction. The contradiction indicates that the assumption is false and the desired conclusion is true

circularity
impossible to define everything without going around in circles


postulate
statement assumed to be true without proof

"determine"
if there are two points, then there is exactly one line that contains them

Pythagorean Theorem
 a^{2}+b^{2}= c^{2}
 (must be a right angle)

Triangle Sum Theorem
the sum of the angles of a triangle is 180^{o}

Circle Theorems
 if the diameter of a circle is d, its circumference is pid
 If the radius of a circle is r, its area is pir^{2}