What is a proof? How do you write a two-column proof?

Answer 1

Proofs are probably something pretty new to you, and it does take time to get a feel for what makes a proof good enough and how you can find the way to prove something. It's really more like writing an essay than like the math you've done before now - more creative and less mechanical. That makes it harder, but also more rewarding and even fun.

A proof is just an orderly way to show that something is true, by building on other things you know are true. The only way that order matters is that each thing you say must be based on something you've already said. Often it will be based on the previous statement, but sometimes you will have to use earlier statements as well. Think of it as building a tower to reach a high goal. Your "givens" are the foundation someone laid for you, and the theorems you have are the girders and rivets you have to put together to make the tower. Let's try drawing your sample proof as a building, to show how its parts are connected...

- Doctor Peterson

Answer 2

i'm not sure if you're referring to 'proof' in terms of geometry but i'll explain it from that perspective

geometry, well i'm sure you know roughly what it is or what it means.. so i won't bore you... anyways, the basis of geometry are postulates(or constant observations), theorems and definitions of geometric figures like lines, points, circles and what not.

Now, these postulates, theorems and definitions are all used to back or support geometric ideas. For example, you're given a rectangle with a diagonal line cutting across it. you're asked to prove that the two triangles formed within the rectangle are congruent ( its lines and angles having the same measure with each other)...

of course you know the two triangles are congruent but you need postulates, theorems and definitions to prove it geometrically... That in essence in proving...

or in short, using given statements (in this case, various postualtes, theorems and definitions) to reach and justify a sound conclusion...

now two column proof, or formal proving is when a method of writing out your statements/ observations in a logical manner in one column, with theorems and statements to support these observations in another column... basically, it's proving using a table method...

the statements that you write have to be logically ordered (starting first from the conditions given then to the implications that they provide) to reach the desired conclusion... it's like baking a cake... you have to follow the steps in the recipe so you can make it correctly...

it was hard trying to explain that in writing... (no wonder my teacher always got so exasperated having to always repeat proving to us) but i hope that helps...

if it's wrong or some parts are simply confusing, just email me... i'd be happy to explain further

Answer 3

A 'proof' is a demonstration that a conjecture is true or correct.

I have no idea at all what you're talking about when you say 'two-column proof'.

Doug

Answer 4

you can write a 2-column proof with STATEMENTS on the left side and REASONS on the right side.