Question

This is not a centralized question, but when writing a proof in geometry how do you know which proofs and theorems to include and in what order?

Answer 1

Let's start by defining what a "theorem" is?

Answer 2

Any ideas?

Answer 3

A theorem is a kind theory that we must prove to be true.

Answer 4

A postulate is a law that is true in any case, and we can use postulates to prove theorems.

Answer 5

That's a good start.

More precisely, a theorem is a statement that is shown to be true by use of a logically developed argument.

So that^ answers your question about. " in what order " you include the statements and their reasons.

They must be presented in a logically developed order, right?

Answer 6

Ya

Answer 7

Now, for the first part of your question:

"...how do you know which proofs and theorems to include..."

Let's define what a "proof" is?

Answer 8

I meant postulate

Answer 9

Ok, so?

Answer 10

But a proof is a sort of list that a person uses to for a variety of things such as proving the congruence between geometric shapes.

Answer 11

Yes, it is definitely "a sort of a list" but there is a formal definition that says:

A proof is logical reasoning that uses:
given facts,
definitions,
properties,
and previously proved theorems
to show that a theorem is true.

Does that^ help answer your question?

Or do you need more :-)

Answer 12

Yes that helps to my answer, thank you very much, so in total when writing my proof I first place a theorem and then a postulate to prove the theorem?

Answer 13

Usually when writing a proof you set up two columns

Statement _____________Reason

Yes, the reasons are usually given facts like postulates etc

And the final step is the theorem you are trying to prove.

Answer 14

Ohhh ok, ok well again thank you.I hope you have a nice day.

Answer 15

Thanks for trying to understand, you have a nice day too :-)