Geometry: Axioms and Postulates
Terms
Addition Axiom
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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
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A quantity is equal to the sum of its parts. A quantity is greater than any one
of its parts.
Reflexive Property
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A quantity is equal to itself.
Substitution Axiom
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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.
