Inequality PostulatesInequality Postulates

If:If:

Reason: The whole is greater than any of its parts.Reason: The whole is greater than any of its parts.

A B C

ACBCAB

Then:Then: ABAC andand BCAC

If:If:

Reason: Transitive postulate of inequalities.Reason: Transitive postulate of inequalities.

Then:Then: CDAB

BCAB andand CDBC

If A>B and C=BIf A>B and C=B

Reason: Substitution postulate of inequalities.Reason: Substitution postulate of inequalities.

Then: A>CThen: A>C

Addition Postulate 1Addition Postulate 1

If A<B and C=D, then A+C<B+DIf A<B and C=D, then A+C<B+D

Reason: When equal quantities are added to unequal Reason: When equal quantities are added to unequal quantities, their sums are unequal in the same order.quantities, their sums are unequal in the same order.

Addition Postulate 2Addition Postulate 2

If A<B and C<D, then A+C<B+DIf A<B and C<D, then A+C<B+D

Reason: When unequal quantities are added to unequal Reason: When unequal quantities are added to unequal quantities, their sums are unequal in the same order.quantities, their sums are unequal in the same order.

Subtraction PostulateSubtraction Postulateof Inequalitiesof Inequalities

If A<B and C=D, then A-C<B-DIf A<B and C=D, then A-C<B-D

Reason: When equal quantities are subtracted from unequal Reason: When equal quantities are subtracted from unequal quantities, their differences are unequal in the same order.quantities, their differences are unequal in the same order.

Reason: Subtraction postulate of inequalitiesReason: Subtraction postulate of inequalities

Multiplication Postulate of =Multiplication Postulate of =

If A<B and C is a positive number, then AC<BCIf A<B and C is a positive number, then AC<BC

Reason: When unequal quantities are multiplied by equal Reason: When unequal quantities are multiplied by equal quantities, their products are unequal in the same order.quantities, their products are unequal in the same order.

Reason: Multiplication postulate of inequalities.Reason: Multiplication postulate of inequalities.

Division Postulate of =Division Postulate of =

If A<B and C is a positive number, thenIf A<B and C is a positive number, then

Reason: When unequal quantities are divided by equal Reason: When unequal quantities are divided by equal quantities, their quotients are unequal in the same order.quantities, their quotients are unequal in the same order.

Reason: Division postulate of inequalities.Reason: Division postulate of inequalities.

C

B

C

A

RememberRemember::

Reason: An exterior angle of a triangle is greater Reason: An exterior angle of a triangle is greater than either of its nonadjacent interior angles.than either of its nonadjacent interior angles.

3

213 mmm

1

2

13 mm andand 23 mm

Exterior angle theorem