Question

What is the key to creating a successful proof?

Answer 1

I know what a proof is, but I could never grasp if there is some type of order on what steps to provide in order to prove something.. I understand that the first step is usually always the given information, and that the last step is to prove what needs to be proven, but I don't understand what the order needs to be in order to actually be able to prove what needs to be proven.

Answer 2

First step is to remember the definitions of the terms that are being discussed. I.E. what is the definition of subset or what is the definition of odd.

Answer 3

logic

Answer 4

Second step is to remember the theorems they have taught recently in class, perhaps even non recent ones if they've been given stress in class

Answer 5

order should be logical but the actual detail of the proof depends on you and the level of your audience

are you talking specifically about proofs in geometryI and II ?

Answer 6

I'm talking about proofs for my Geometry class.
I just don't understand the order, I suppose.

Answer 7

Third step is to remember the non-direct methods of proof, such as proof by contradiction or proof by contrapositive.

Answer 8

Geometry proofs?

Answer 9

Yeah, geometry really makes no sense to me. :p

Answer 10

Usually it make sense what the order is...

Answer 11

Like, you have to wake up before you brush your teeth because you can't brush your teeth while you are asleep

Answer 12

-.-
just memorize these stuff

Answer 13

Your Z and F shape seem to be the same?

Answer 14

Yeah, I understand sort-of what the last steps should be, but it's the first and middle steps don't really make much sense to me.

Answer 15

so , if u remember such basic stuff , steps wont be a problem

Answer 16

@wio yes lol
but kids dont know :P

Answer 17

Yeah, but we have more theorems and stuff to try to memorize each day ;p @Marki

Answer 18

trust me, it makes no sense to anyone the first time

it helps to know about below concepts as you will be using them as reasons in almost all your proofs in geometryI and II :
```
1) betweenness axiom
2) algebraic properties of equality
3) vertical angles theorem
4) transversal properties
5) triangle sum property
```

Answer 19

:D memorize those would be enough

Answer 20

and you have triangle similarity and congruence postulates

Answer 21

yeah trust him :D

Answer 22

and a zillion other things .. but 95% of the proofs in your geometry class use above listed stuff as "reasons"

Answer 23

Thanks!! ^.^
What is that first thing, though? I've never heard of it. o-o

Answer 24

leave it , u wont use it

Answer 25

Okay xD

Answer 26

yeah betweenness axiom is an very important property but it comes very rarely in your proofs so dont bother about it for now

Answer 27

whats your favorite proof in geometry so far ?

Answer 28

using it u can make advanced proofs , also u can proof alternate theorem

Answer 29

Alright, thank you so much! You guys are awesome! ^.^
And hmmm, I dunno, I'm terrible at proofs. xD

Answer 30

lets prove vertical angles theorem ?

Answer 31

prove vertical angles are congruent

Answer 32

Well, I know that there is a theorem that states "vertical angles are congruent", so I would use that, right?

Answer 33

that would be like saying "I am beautiful because I am beautiful"
it doesn't prove anything.

Answer 34

here is the proof from khan, watch it when free
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/ang_intro/v/proof-vertical-angles-are-equal

notice what definitions/theorems he uses as reasons

Answer 35

Okay, I will watch it.
Thanks again! ^.^

Answer 36

"I am beautiful because it does not need a proof :D
(Axiom)

Answer 37

Haha, good one!! XD