Theorems
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In geometry, deductive rules can be used to prove conjectures.
The first rule of geometry..... do not talk about geometry. The second rule of geometry..... DO NOT TALK ABOUT GEOMETRY hahah But seriously you'll have to be a bit more specific here cos there's too many geometric rules to list!
No. The rules of two dimensional geometry can only be used for two dimensional geometry. You can take the basic principles of two dimensional geometry and alter them slightly to be able to apply to three dimensional solids
No. Postulates are the foundations of geometry. If you said they were wrong then it would be saying that Euclidean geometry is wrong. It is like if you asked how do we know that English is right. It is how the English language works. So no postulates do not need to be proven.
Euclid put the rules on a systematic and axiomatic basis.