TITLE: Some theorems in euclidean geometry have incomplete proofs
QUESTION [6 upvotes]: I have seen that, in euclidean geometry, proofs of some theorems use one instance of the 'geometric shape'(on which the theorem is based) to proof the theorem. 
Like,  the proof of 'A straight line that divides any two sides of a triangle proportionally, is parallel to the third side' use only one instance of a triangle---like:
∆ABC is the instance
Then, constructions are added to this diagram to prove the theorem.
Clearly, the proof is not general.Because, only a triangle is in view. 
Therefore, this proof is not precise.
We have had a general proof, must be having.I haven't yet visualized what the general proof might be.
So, why do people call the above type of proof ,a proof?Is it a complete mathematical proof?

REPLY [3 votes]: This is and is not a problem.
The proof is in the words, not the diagram.  The diagram merely suggests which words to use, or illustrates steps in the proof that would otherwise be hard to follow.  Once a proof is written down, the diagram is logically irrelevant and not part of the proof.  In this sense the diagram cannot have any effect on the validity of the demonstration.
A proof inspired by a limited or inaccurate set of diagrams can overlook some possible cases or make invalid assumptions about the position of objects in the diagram.   This is not as big a problem as it might appear to be, because proofs that are correct for the cases depicted by some (accurately drawn) diagrams, can often be interpreted in ways that cover the general case, such as allowing negative values for length, area and angle measurements.