Every step of a proof plays a precise logical role. Recognising the type of each step helps to write it in an orderly way and to read it without getting lost.
Remark — The types of logical step
- Hypothesis: starting datum, what is known.
- Thesis: what one wishes to prove.
- Construction: an auxiliary element introduced in the drawing (a segment, a parallel, an altitude…).
- I observe: a fact noticed directly from the figure or from the definition.
- I consider: a specific object is examined (a triangle, an angle, a segment).
- Key idea: the central insight of the proof.
- I deduce: a logical conclusion following from the previous steps.
- Similarly: the same reasoning is repeated on another object.
- Verified: an established result, which can be used in the following steps.
The symbol (or the abbreviation q.e.d.) marks the end of the proof.
Links
Topics: Euclidean geometry
Concepts: Proof · Hypothesis and thesis
Skills: Proving