Friday, October 10, 2008

Geometry Chapter 3 - Sections 3.5 - 3.8 - 2008 - 2009

3.5 - 3.8 Postulates, Theorems and Proof:

I. Postulate or axiom - a true obvious statement and accepted without proof.
- is a statement whose truth is accepted without proof.

II. Theorem - is a statement that is proved by deductive reasoning.

III. Postulates:

A. Reflexive Postulate: angle A = angle A : everything is congruent to itself

B. Symmetric Postulate: if angle A = angle B then angle B = angle A (somewhat like the converse)

C. The Substitution Postulate: a quantity may be substituted for its equal in any statement of equality.

Example: if x = y and y = 8, then we can conclude by substitution that x = 8.

D. Partition Postulate: a whole is equal to the sum of the parts (part + part = whole)

E. Addition Postulate: if a = b and c = d, then a + c = b + d

F. Subtraction Postulate: if a = b and c = d, then a - c = b - d

G. Multiplication Postulate: if a = b and c = d, then ac = bd

H. Division Postulate: if a = b and c = d, then a/c = b/d.

I. Power Postulate: if a = b then a2 = b2

One of my students thought this would be a better way:

if a = b and c = d then ac = bd

Does anyone see a flaw in this?

J. Roots Postulate: if a = b and a is positive, then the square root of a = the square root of b

Example using a proof: