There are two types of proof:
Direct proofs: Where it is proved (deduced or induced) from the basic axioms, definiyions or earlier proved theorems that the statement is correct.
Indirect proofs: The principle for this type of proofs is that it is proved that the opposite of the stated proposition cannot be true since this would lead to a contradiction or to something impossible.
In order to solve a geometrical problem it is often necessary to perform geometrical construction. This means e.g that the solution may be facilitated by
connecting given dots
extrapolate given lines
Bisect given lines or angles in halves,
Construct a line parallell to a given line
Constuct a line perpendicular to a given line.
construct circles etc.
Euclid then proceeds to define the equal-sign (2+3 =5), inequality sign ( A > B) and what is meant by addition (the sum of parts) and multiplication )repeated adition of the same number (A +A +A = 3A) and the difference between two quantitites A – B which eguals the quantity you must add to B to get A. .