postulates 2-2b what are some facts that are accepted without proof? who organized much of geometry...
TRANSCRIPT
Postulates 2-2B
What are some facts that are accepted without proof?
Who organized much of geometry and other
mathematics into a deductive system?
Properties of Equality
*Reflexive Property a=a
*Symmetric Property If a=b ,then b=a
*Transitive Property If a=b and b=c, then a=c
Addition Property If a=b, then a+c=b+c
Multiplication Property If a=b, then ac=bc
Properties of Addition & Multiplication
Associative Properties a+(b+c)=(a+b)+c
*(group) a(bc)=(ab)c
Commutative Properties a+b=b+a
*(commute—move) ab=ba
Distributive Property a(b+c)=ab+ac
State the property of real numbers that justifies each statement.
AB+CD = CD+AB
Commutative Property of Addition (move)
If x−20=44, then x−20+20=44+20
Addition Property of Equality
Euclid• Greek mathematician• Wrote The Elements
around 300BC• Organized geometry
& other maths into a deductive system.
• Called basic assumptions—self-evident truths
• Self-evident truths=postulates
Questions????What is the smallest number of points through
which only one line can be drawn?
Questions????
Three points, A, B, and C are not all on the same line. How many planes contain all three of the points?
A
B
CP
Questions????
What does the intersection of two planes look like?
Questions????
If a plane contains two points of a line, must it contain the whole line?
Questions????
What is the smallest number of points that cannot be contained in just one plane?
AB
C
P
Definition
Space is the set of all points
Points-Existence PostulateSpace contains at least four noncoplanar
points. Every plane contains at least three noncollinear points. Every line contains at least two points.
Straight-Line Postulate
Two points are contained in one and only one line. (Two points determine a line.)
Plane Postulate
Three noncollinear points are contained in one and only one plane. (Three noncollinear points determine a plane.)
1
2
3
Flat-Plane Postulate
If two points are in a plane, then the line containing the points is in the same plane.
1
2
Plane-Intersection Postulate
If two planes intersect, then their intersection is a line.
State the postulate or postulates that justify each statement. Use
page 116.
If l contains A and B, then there is no other line that contains these points.
Straight-Line PostulateIf points H and K lie in plane R, then HK lies
in plane R.Flat-Plane PostulateA plane contains at least one line.Points-Existence Postulate, Flat-Plane
Postulate
Assignment 2-2B
Page 117, 1-8, 20, 22, 24.