Mathematics is a deductive system in which one starts from some definitions, some undefined terms and some self-evident truths (which may be based on experience) called axioms. Writing proofs in geometry implies argument or justification of statements.

• As in all mathematical theories, Euclid built a theory involving some abstract objects and relationships between them. Some of the objects are undefined, for example, 'point', 'line', etc. Others are defined in terms of these objects. Of course, the effort is to keep the number of undefined terms to a minimum.
• Each theorem in Euclid's geometry is proved from some preceding results. Of course, he started with a set of five assumptions about the undefined terms, which are the axioms or postulates of the theory. Any set of statements can be laid down as postulates so long as they do not lead to any logical contradictions or inconsistencies. Obviously, the fewer the postulates, the better. Mathematicians try to derive more and more theorems from fewer and fewer postulates. 

Thus from the above-mentioned points, it is clear that writing proofs in geometry imply argument or justification of statements.