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.
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: