Inequality Postulates. If: Reason: The whole is greater than any of its parts. ABC Then: Then:and.

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Presentation transcript:

Inequality Postulates

If: Reason: The whole is greater than any of its parts. ABC Then: Then:and

If: Reason: Transitive postulate of inequalities. Then: Then: and

If A>B and C=B Reason: Substitution postulate of inequalities. Then: A>C Then: A>C

Addition Postulate 1 If A<B and C=D, then A+C<B+D Reason: When equal quantities are added to unequal quantities, their sums are unequal in the same order.

Addition Postulate 2 If A<B and C<D, then A+C<B+D Reason: When unequal quantities are added to unequal quantities, their sums are unequal in the same order.

Subtraction Postulate of Inequalities If A<B and C=D, then A-C<B-D Reason: When equal quantities are subtracted from unequal quantities, their differences are unequal in the same order. Reason: Subtraction postulate of inequalities

Multiplication Postulate of = If A<B and C is a positive number, then AC<BC Reason: When unequal quantities are multiplied by equal quantities, their products are unequal in the same order. Reason: Multiplication postulate of inequalities.

Division Postulate of = If A<B and C is a positive number, then Reason: When unequal quantities are divided by equal quantities, their quotients are unequal in the same order. Reason: Division postulate of inequalities.

Remember : Reason: An exterior angle of a triangle is greater than either of its nonadjacent interior angles and and Exterior angle theorem