Question

In the diagram below, all four right triangles are congruent and the interior quadrilateral is a square.

Answer 1

When written in the correct order, the paragraph below proves the Pythagorean Theorem using the diagram.

Let a represent the height and b represent the base of each triangle.

The area of one triangle is represented by the expression One halfab.

(1) The length of a side of the interior square is (a – b).

(2) The area of all four triangles will be represented by 4 • One halfab or 2ab.

(3) The area of the interior square is (a – b)2.

(4) By distribution, the area is a2 – 2ab + b2.

The area of the exterior square is found by squaring side c, which is c2, or by adding the areas of the four interior triangles and interior square, 2ab + a2 – 2ab + b2.

Therefore, c2 = 2ab + a2 – 2ab + b2.

Through addition, c2 = a2 + b2.

Which is the most logical order of statements (1), (2), (3), (4) to complete the proof?

Answer 2

http://math.stackexchange.com/questions/103758/pythagorean-theorem-proof-without-words-request-for-words

i guess you mean this

Answer 3

yeah, it looks about the same, but I'm having trouble understanding it

Answer 4

it's just an arrangement of those triangles.
try to see the matching colour ... and they are all congruent.

Answer 5

okay, i see that now... but the question gave me 4 statements that I have to put into logical order.

(1) The length of a side of the interior square is (a – b).
(2) The area of all four triangles will be represented by 4 • One halfab or 2ab.
(3) The area of the interior square is (a – b)2.
(4) By distribution, the area is a2 – 2ab + b2

Answer 6

this might take a time ... i have not read your question at all.

Answer 7

ok

Answer 8

wow ,,, it was quite different, and elegant proof.

Answer 9

i think they are in logical order

Answer 10

uh

Answer 11

ok

Answer 12

but i think the logical order (for solving the problem with) could be 2, 1, 3, 4.

Answer 13

well, i think it fits, fist triangle and ... square later. though i think ... i wouldn't matter as long as calculation is concerned.

Answer 14

it's not really concerned with calculation, just logic. but thanks.

Answer 15

didn't do a thing.
you are most welcome.

Answer 16

@experimentX i have the same problem but i dont seem to understand what u guys are talking about

Answer 17

nothing ... just order in which proof must be written

Answer 18

ummmm ooook, not really helping but ok...

Answer 19

it's like fist you wake up in morning then you have break fast and then you go to school.
similarly ... you have to prove things in similar way. first this and then that .. and then that ... logic flowing like water in river.

Answer 20

okk.... thanks