What is the difference between a Definition and a Theorem? This may get into a discussion, but I have a homework problem and it tells me there is a difference between a definition and a theorem.  I don't know how to differentiate the two in this question:
Consider the domain of all quadrilaterals.  Let
A(x) = "x has four right angles."
R(x) = "x is a rectangle."
Write the meaning of each mathematical statement in the predicate logic, keeping in mind the logical distinction between definitions and theorems.
(a) Definition. A quadrilateral is a rectangle if it has four right angles.
(b) Theorem. A quadrilateral is a rectangle if it has four right angles.

A definition describes the exact meaning of something, whereas a theorem proves something.
