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- anonymous

Given:
Square with side c.
All four interior triangles are right triangles.
All four interior triangles are congruent.
The interior quadrilateral is a square.
Prove:
a2 + b2 = c2

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- anonymous

- schrodinger

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- anonymous

When written in the correct order, the sentences below create a paragraph proof of 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 area of the interior square is (a – b)2.
(2) The length of a side of the interior square is (a – b).
(3) By distribution, the area is a2 – 2ab + b2.
(4) The area of all four triangles will be represented by 4 • One half ab or 2ab.
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), and (4) to complete the proof?
(4), (1), (2), (3)
(4), (2), (1), (3)
(4), (2), (3), (1)
(4), (1), (3), (2)

- ganeshie8

it CANNOT start with (4)

- ganeshie8

makes no sense to me , check ur options once

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- anonymous

That's all the choices I have

- ganeshie8

oops- pls disregard... it does start with (4)

- anonymous

lol will do

- ganeshie8

we have base of triangle = b
height = a
so we can find area of triangle, and since all four triangles are congruent, we can find area of all 4 triangles by multiplying (1/2)ab by 4
(1/2)ab * 4 = 2ab
(4),...
next what

- ganeshie8

we can find the side of inner-square

- anonymous

Oh

- ganeshie8

its (a-b)
next, area of square (a-b)^2
next.. ?

- anonymous

Not sure.

- ganeshie8

second statement would be length of square, right ?

- anonymous

Length?

- anonymous

You beat me...

- ganeshie8

lol, see the diagram, we can find length of side of square, by subtracting b from a
length = (a-b)

- ganeshie8

so, (2) is the correct one in the sequence

- anonymous

Yep

- ganeshie8

once we knw length of side of a square,
cant we find its area ?

- anonymous

Yes so then 1?

- ganeshie8

|dw:1347544885906:dw|

- ganeshie8

yes

- anonymous

4, 2, 1, 3?

- ganeshie8

Correct !

- anonymous

Thanks

- ganeshie8

yw! :)

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