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Question

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jim_thompson5910 · Answer

which one do you think it is and why?

larseighner · Answer

Hint:  Both the diagrams can be used to make a valid proof.  So, you need to look at the steps.

anonymous · Answer

Sean is correct and so is Gina. 
Both of their work is correct.

anonymous · Answer

@jim_thompson5910 and @LarsEighner

jim_thompson5910 · Answer

what is (a-b)^2

larseighner · Answer

I don't think so.  Scrutinize each of the steps.

anonymous · Answer

I was stuck between options and that was the best choice, at least I thought :/ . 

a^2-2ab + b^2

anonymous · Answer

$$a^2-2ab+b^2$$

jim_thompson5910 · Answer

look at what sean gets for (a-b)^2

larseighner · Answer

But that contradicts step 2 of Sean's proof.

larseighner · Answer

What is more, look at his Step 1.  What is the area of one of the triangles?

anonymous · Answer

Sean is incorrect.

anonymous · Answer

^Step 2 .

larseighner · Answer

Yes.  As an excercise you might correct his argument.  But for purposes of this answer he is wrong.

larseighner · Answer

He got to his conclusion by making two error which compensated for each other.  But if you correct both, you can construct a valid argument with his diagram.

anonymous · Answer

For sure I know Sean is incorrect, I'm trying to figure out Gina right now.

anonymous · Answer

The options are minimized to C and D right now.

larseighner · Answer

Has Gina correct stated the area of the big square?

anonymous · Answer

I want to know where the 2ab part comes from?

larseighner · Answer

In step 1 it comes from algebra.  It is the expansion of the square of the sum a + b.

In step 2, you have to figure the area of a right triangle with legs a and b (which gets multiplied by 4, because there are 4 small triangles which are congruent.

anonymous · Answer

Gina is correct.

larseighner · Answer

Yes. This is a famous proof.  Socrates (according to Plato) elicited this proof from a slave by asking the slaves questions.  (However, Socrates was not trying to prove Pythagoras.  He was trying to prove that everyone altready knows everything -- you just have to ask them the right questions to get the knowledge out of them.)

anonymous · Answer

O.O Ah, so wise; very interesting  and very effective.

In conclusion,  Gina is correct and Sean is incorrect= C.

larseighner · Answer

Right.

anonymous · Answer

Thank you, I appreciate all your help . :)

larseighner · Answer

You are most welcome.