1. Postulates 2-2B What are some facts that are accepted without proof? Who organized much of geometry and other mathematics into a deductive system?

2. 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

3. Properties of Addition & Multiplication Associative Propertiesa+(b+c)=(a+b)+c *(group)a(bc)=(ab)c Commutative Propertiesa+b=b+a *(commute—move)ab=ba Distributive Propertya(b+c)=ab+ac

4. 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

5. 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

6. Questions???? What is the smallest number of points through which only one line can be drawn?

7. 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 C P

8. Questions???? What does the intersection of two planes look like?

9. Questions???? If a plane contains two points of a line, must it contain the whole line?

10. Questions???? What is the smallest number of points that cannot be contained in just one plane? A B C P

11. Definition Space is the set of all points

12. Points-Existence Postulate Space contains at least four noncoplanar points. Every plane contains at least three noncollinear points. Every line contains at least two points.

13. Straight-Line Postulate Two points are contained in one and only one line. (Two points determine a line.)

14. Plane Postulate Three noncollinear points are contained in one and only one plane. (Three noncollinear points determine a plane.) 123

15. Flat-Plane Postulate If two points are in a plane, then the line containing the points is in the same plane. 1 2

16. Plane-Intersection Postulate If two planes intersect, then their intersection is a line.

17. 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 Postulate If points H and K lie in plane R, then HK lies in plane R. Flat-Plane Postulate A plane contains at least one line. Points-Existence Postulate, Flat-Plane Postulate

18. Assignment 2-2B Page 117, 1-8, 20, 22, 24.