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# What Is Proven With a Geometric Proof?

**Theorems are proven with geometric proofs.** Theorems are statements that have proven to be true though the application of other theorems and statements. Theorems can be proven through the application of accepted mathematical operations and arguments.

Theorems are the embodiment of a general mathematical principle presented in simplest form. They can be combined and built upon to create complex mathematical models that describe the behavior of a system. Theorems can also be built on other generally accepted mathematical truths called axioms, which serve as the premise, or starting point, for a certain line of reasoning. Axioms are premises that are so evident, they can be accepted as true without controversy.

Theorems are proven through the application of logical arguments that reach a well-defined conclusion through deductive reasoning. The geometric proof of a theorem is justification for the truth of the theorem statement. The conclusions that are deduced through the proof of a theorem are called hypotheses and should be interpreted as truth if the deductive means to arrive at these conclusions are sound.

Mathematical theorems should not be confused with scientific theories.The former are based on deductive logic and reasoning, whereas the latter are based on empirical observation and validation.

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