DefinitionGeometric proofs are deductive arguments that use geometric principles, definitions, and theorems to prove that the assertions (conjectures) they set out to prove are true. A geometric proof is a method of establishing the truth of a geometric statement, using logical reasoning based on definitions, axioms (or postulates), and previously proved theorems (proofs). A geometric proof uses a base set of axioms and an unlimited number of derived theorems, which may not be available with an established proof technique. Geometric proofs are a foundation on which all other geometry weaves (and likewise builds up) so as to construct mathematical knowledge on both the deeper understanding of conic sections and other elements of geometry shapes. For instance, in order to demonstrate the Pythagorean theorem, a2+b2=c2 for a right triangle with sides a, b, and c, one may provide a proof by geometry that uses the construction of squares on each side of the triangle and demonstrate that areas of the squares conform to the relation.
