**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 a

^{2}= b

^{2}

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

if a = b and c = d then a

^{c}= b

^{d}

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:**