In a mathematics sense, yes, theorems always require proofs. A theorem is usually just a statement about how something works of relates to another area or operation or idea etc. to actually be able to use the theorem without any doubt, it has to be proved Not necessarily by the person who came up with the theorem, but it must be proved before it can be used.
The same can also be said of corollaries and lemmas.
Geometric proofs help you in later math, and they help you understand the theorems and how to use them, they are actually very effective.
Euclid (http://en.wikipedia.org/wiki/Euclid)
the application of statistical and mathematical techniques , theorems and proofs in understanding geographical systems is known as the quantification in geography.
The statements that require proof in a logical system are theorems and corollaries.
The statements that require proof in a logical system are theorems and corollaries.
Corollaries,TheoremsCorollaries, Theorems
Theorems are statements in geometry that require proof.
Postulates and axioms are accepted without proof in a logical system. Theorems and corollaries require proof in a logical system.
In mathematics, deductive reasoning is used in proofs of geometric theorems. Inductive reasoning is used to simplify expressions and solve equations.
6 theorems
There are a great number of different proofs of the Pythagorean Theorem. Unfortunately, many of them require diagrams which are hard to reproduce here. Check out the link to Wikipedia's page on the theorem for several different proofs.
Starting from around 3rd-4th grade, you start to learn really basic geometry. But around 8th or 9th grade, you actually start to learn more advanced geometry that uses theorems and postulates and proofs.