Terms:

Geometry (plane or Euclidean) is a branch of Mathematics that studies figures.

An axiom is a truth obvious by itself whish is susceptible of any proof.
Example: A triangle has three sides.

A postulate is a truth that we don't know proving; and we admit as true in order to support the continuation of a reasoning.
Example:
The ligne is the shortest path between two points.

A theorem is a statement of truth that we establish by the means of a proof. A statement of proof includes: a hypothesis, a conclusion, and a proof (we assume, and conclude what is going to be proven).
Example:
Pythagoras' theorem.

A corollary is a consequence that comes from the proof a theorem.
Example:
The hypotenuse is larger than the legs in a rectangular triangle .

A lemma is a truth that we have already proven in order to support the continuation of a reasoning. We know proving a lemma, but not a postulate.
Example:
Jordan's lemma.

A preposition is a the statement of an axiom, postulate, theorem, corollary, or a lemma.