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.