The law of detachment A -->B
The law of contrapoitive Not B --> Not A
The law of syllogism a --> b, b-->c, therefore a --> c
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Geometry is based on logic.
logic postulates theorems
Geometry, unlike science, doesn't really have laws, it has theorems, and many different mathematicians contributed to the creation of the basic theorems of geometry. Perhaps the best known is Pythagoras.
Elements
Elements