Math Chapter 1 and 2

method used for drawing conclusions from a limited set of observations. General----> Specific

logic to draw conclusions from statements already accepted as true.

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

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

part of a line thats bounded by two end points

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

points contained by the same line

points that contained in the same plane

points not on a single line

lines that contain a common point

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

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

• lies in a plane
• bounded by line segments
• two dimensional

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

• sume of the lengths of its sides
• measured in units

surface included in square units or units²

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

created with straightedge and compass

to divide into two equal parts

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

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

the letter a or "if"

the letter b or "then"

uses circles to illustrate how conditional statements relate to each other

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

statement formed by interchanging the a and b and denying both

formed by denying both a and b

• an argument in the from
• a--> b
• b--> c
• a-->c

argument of syllogism

statements of the arguement

conncets the first to the last

statement that is proved by reasoning deductively from already accepted statements

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

impossible to define everything without going around in circles

• point
• line
• plane

statement assumed to be true without proof

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

• a²+b²= c²
• (must be a right angle)

the sum of the angles of a triangle is 180^o

• if the diameter of a circle is d, its circumference is pi-d
• If the radius of a circle is r, its area is pi-r²