Chapters 1&2 Flashcards
Numbers 1 digit apart
Consecutive
Cannot prove or disprove
Postulate
mathmatical statements
Theorems
Point, line, and plane
Undefined Terms
Location (typically a dot)
Point
Straight ____, infinite number of points
Line
Flat surface that continues forever
Plane
group/collection of items, numbers, objects, etc.
Set
Name for items that belong to a set
Element
C: If one set contains every element of another set, then the second set is a _____
Subset
What does ∈ mean?
Element of
{ } or ∅: A set that has no elements
Empty set or Null set
Two sets are ____ if they contain the exact same elements
Equal
∪ means _____ and “or” (The elements of two sets together into one)
Union
∩ means _____ and “and” (Includes all common (elements in BOTH sets) elements)
Intersection
Two sets ______ if there are one or more elements that are common to the sets
Intersect
{1, 2, 3, 4, 5, … }
Natural Numbers
{0, 1, 2, 3, 4, 5, … }
Whole Numbers
{….-2, -1, 0, 1, 2, …}
Integers
Any number in the form p/q where p,q ∈ integers and q ≠ 0 (ex. 1/2, 0.4, 0.51)
Rational Number
Cannot be written as a fraction (ex. π, √, e) , not rational
Irrational Number
For every x and y, one and only one of the following properties holds: x(less than)y,x=y, or x(greater than)y
Trichotomy Property
Every positive number has exactly one positive square root
Existence of Square Roots Property
a+b = b+a
Commutative Property of Addition
ab = ba
Commutative Property of Multiplication
(a+b)+c = a+(b+c)
Associative Property of Addition
(ab)c=a(bc)
Associative Property of Multiplication
a(b+c)=ab+ac
Distributive Property
If a=b and c=d, then a+c=b+d
Addition Property of Equality
If a=b and c=d, then a-c=b-d
Subtraction Property of Equality
If a=b and c=d, then ac=bd
Multiplication Property of Equality
If a=b and c≠0, then a/c=b/c
Division Property of Equality
If a=b and b=c, then a=c
Transitive Property of Equality
If x(less than)y and y(less than)z, then x(less than)z
Transitive Property of Inequalities
If a(less than)b and x(less than or equal to), then a+y(less than)b+y
Addition Property of Inequalities
If x(less than)y and a(greater than)0, then ax(less than)ay
Multiplication Property of Inequalities
Distance is always positive
The Distance Postulate
Thousandth, 1/1000
Milli(m)
Hundreth, 1/100
Centi (c)
Tenth, 1/10
Deci (d)
Ten, 10
Deca (da)
Hundred, 100
Hecto (h)
Thousand, 1000
Kilo (k)
The points of a line can be placed in correspondance with the real number system in a way that:
1. Every point of the line corresponds with one real number
2. Every real number corresponds with a point on the line
3. Distance between any two points is the absolute value of the difference of their corresponding real numbers
Ruler Postulate
The sort described in the ruler postulate is called a _____
Coordinate System
The number corresponding to a given point is called its _____
Coordinate
The coordinate of P is 0 and Q is a positive
Ruler Placement Postulate
Definition:
Point B is ___ A and C if:
1. A, B, C are different, collinear points
2. AB + BC = AC
When B is between A and C, we write “A-B-C” or “C-B-A”
Between
Let A, B, and C be points of a line with X,Y,Z respectively. If X(less than)Y(Less than)Z, then A-B-C
Theorem 2-3
If A,B, and C are 3 different collinear points, then exactly one of them is between the other two.
Theorem 2-4
Two points detwermine a line written as AB (Line on top of AB)
The Line Postulate or Theorem 2-5
If B-A-C, then AB and AC are opposite rays
-Two collinear rays whose only intersection is a common endpoint
Opposite Rays
Let AB be a ray and X a positive number. There is exactly one point, P, on AB such that AP=X
Point-Plotting Theorem
A point B is called the _____ of AC (Segment) if:
1. A-B-C
2. AB=BC
Midpoint
Every segment has exactly one midpoint
Midpoint theorem
The midpoint of a segment is said to _____ the segment
Bisect
The midpoint of a segment or any segment, ray, line, or plane which contains the midpoint but not the segment is a _____ of it.
Bisector
“In that order”
Respectively
Euclid, a famous Greek mathematician known as the “Father of Geometry” in 300 B.C., wrote his ideas into a book. What was the name of this book?
“The Elements”
Finding subsets:
2^n
