You start out with things that you know and use them to make logical arguments about what you want to prove. The things you know may be axioms, or may be things you already proved and can use.
The practice of doing Geometry proofs inspires logical thinking, organization, and reasoning based on facts. Each statement must be supported with a valid reason, which could be a given fact, definitions, postulates, or theorems.
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Euclid
Obviously?...
The book Elements contained axiomic proofs for plane geometry.
Geometry is the mathematical study and reasoning behind shapes and planes in the universe. Geometry compares shapes and structures in two or three dimensions or more. Geometry is the branch of mathematics that deals with the deduction of the properties, measurement, and relationships of points, lines, angles, and figures in space from their defining conditions by means of certain assumed properties of space. The mathematics of the properties, measurement, and relationships of points, lines, angles, surfaces, and solids. Plane geometry is traditionally the first serious introduction to mathematical proofs. A drawing of plane figure usually a nice picture of what has to be proved, so it is a good place to start leaning to make and follow proofs. One present proofs in plane geometry by chart showing each step and the reason for each step.
Postulates are statements that prove a fact. An example would be that 2 points create a line segment. You usually use postulates in proofs.