Question

what is the difference between a postulate and theorem in geometry

Answer 1

A postulate is something you assume to be true. Sometimes these are called "axioms." For example, we assume things like A straight line may be drawn from any given point to any other.

Answer 2

A corollary is something that is true, derived from a theorem in a trivial way. For example, we prove that triangles are congruent based on their sides all being equal.