General Postulates Duducive Proofs................................................................................................

(Substitution Postulate of Equality) A number may be substituted for its equal in an expression.

Example: If A=B then A or B may be substituted for each other.

Therefore, if x = y then x + 2y = 4 then you can replace the (x) with a (y) in the equation

x + 2y = 4 using the substitution postulate of equality to obtain the equation y + 2y = 4 by simplifying we get 3y = 4 and simplification even further gives us the solution that y = 4/3

(Reflexive Postulate of Equality) Any number equals itself.

Example: If A=A then A will always equal A

Therefore, 2 = 2 or 4 = 4

Note: The reflexive postulate is usually used before exercising the subtraction postulate or the transitive postulate.

(Symmetric Postulate of Equality) The members of an equation may be interchanged.

Example: If a = b then b = a
Example: If x + y = 180 then 180 = x + y

Therefore, 90 + 90 = 180 then 180 = 90 + 90

(Transitive Postulate of Equality) Numbers equal to the same number are equal to each other.

Example: If a = b and b = c then a = c

Therefore, if A + B = 180 and C + B = 180
Then, B = B (Reflexive postulate) and
A = C (Transitive postulate)

(Addition Postulate of Equality) If equal numbers are added to equal numbers, the sums are equal.

Example: If a = b and c = d then, a + c = b + d

Therefore, 2 + 2 = 3 + 3 then, 2 + 3 = 2 + 3

(Subtraction Postulate of Equality) If equal numbers are subtracted from equal numbers, the differences are equal.

Example: If a = b and c = d then, a – c = b – d

Therefore, 4 + 4 = 5 + 5 then, 4 – 5 = 4 – 5

(Multiplication Postulate of Equality) If equal numbers are multiplied by equal numbers, the products are equal.

Example: If a = b and c = d then a*c = b*d

Therefore, if ½ A = 45 and 2 = 2
Then, A = 45

(Division Postulate of Equality) If equal numbers are divided by nonzero numbers, the quotients are equal.

Example: If a = b and c = d then a/c = b/d

Therefore, if 2A + 2B =180 and 2 = 2
Then, A + B = 90

(Powers Postulate of Equality) Like powers of equal numbers are equal.

Example: If a = b then, aⁿ = bⁿ

(Roots Postulate of Equality) Like roots of equal numbers are equal.

Example: If a = b then √a = √b