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# Geometry: Axioms and Postulates

### Contents

#### Terms

Addition Axiom  -  If equals are added to equals, their sums are equal. If unequals are added to equals, their sums are unequal.
Division Axiom  -  If equals are divided by equals, their quotients is equal. If unequals are divided by equals, their quotients is unequal.
Multiplication Axiom  -  If equals are multiplied by equals, their products are equal. If unequals are multiplied by equals, their products are unequal.
Partition Axiom  -  A quantity is equal to the sum of its parts. A quantity is greater than any one of its parts.
Reflexive Property  -  A quantity is equal to itself.
Substitution Axiom  -  Equals can be substituted for each other in any equality or inequality.
Subtraction Axiom  -  If equals are subtracted from equals, their differences are equal. If unequals are subtracted from equals, their differences are unequal.
Transitive Property  -  If two quantities are equal to a third quantity, they are equal to each other. If a quantity is greater than another quantity, which is greater than a third quantity, then the first quantity is greater than the third quantity.