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postulate/axiom

a statement whose truth is accepted without proof

powers postulate

the squares of equal quantities are equal

proof

is a valid arguement that establishes the truth of a statement

reflexive property of equality

a quantity is equal to itself

substitution postulate

a quantity may be substituted for its equal in any statement of equality

subtraction postulate

if equal quantities are subtracted from equal quantities the differences are equal

symmetric property of equality

an equality may be expressed in either order

theorem

a statement that is proved by deductive reasoning

transitive property of equality

quantities equal to the same quantity are equal to each other