In geometry one does not calculate: one proves. The result of a proof is called a theorem, and it is always built in the same way: one starts from some facts taken as true and arrives, step by step, at establishing new ones.
Definition — Theorem
A theorem is a chain of reasoning that starts from a set of known facts taken for granted, called hypotheses (Hp), in order to prove, in a necessary and inescapable way, new facts, called the thesis (Th).
The arrow reads “implies”: if the hypotheses hold, then the thesis necessarily holds. Distinguishing clearly what is given (Hp) from what is to be proved (Th) is the first step of every proof.
Links
Topics: Euclidean geometry
Concepts: Proof · Hypothesis and thesis · Theorem
Skills: Proving