anonymous
  • 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
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • 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)
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ganeshie8
  • ganeshie8
it CANNOT start with (4)
ganeshie8
  • ganeshie8
makes no sense to me , check ur options once

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anonymous
  • anonymous
That's all the choices I have
ganeshie8
  • ganeshie8
oops- pls disregard... it does start with (4)
anonymous
  • anonymous
lol will do
ganeshie8
  • 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
  • ganeshie8
we can find the side of inner-square
anonymous
  • anonymous
Oh
ganeshie8
  • ganeshie8
its (a-b) next, area of square (a-b)^2 next.. ?
anonymous
  • anonymous
Not sure.
ganeshie8
  • ganeshie8
second statement would be length of square, right ?
anonymous
  • anonymous
Length?
anonymous
  • anonymous
You beat me...
ganeshie8
  • ganeshie8
lol, see the diagram, we can find length of side of square, by subtracting b from a length = (a-b)
ganeshie8
  • ganeshie8
so, (2) is the correct one in the sequence
anonymous
  • anonymous
Yep
ganeshie8
  • ganeshie8
once we knw length of side of a square, cant we find its area ?
anonymous
  • anonymous
Yes so then 1?
ganeshie8
  • ganeshie8
|dw:1347544885906:dw|
ganeshie8
  • ganeshie8
yes
anonymous
  • anonymous
4, 2, 1, 3?
ganeshie8
  • ganeshie8
Correct !
anonymous
  • anonymous
Thanks
ganeshie8
  • ganeshie8
yw! :)

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