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BIGDOG96

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

  • one year ago
  • one year ago

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  1. BIGDOG96
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    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)

    • one year ago
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  2. ganeshie8
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    it CANNOT start with (4)

    • one year ago
  3. ganeshie8
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    makes no sense to me , check ur options once

    • one year ago
  4. BIGDOG96
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    That's all the choices I have

    • one year ago
  5. ganeshie8
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    oops- pls disregard... it does start with (4)

    • one year ago
  6. BIGDOG96
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    lol will do

    • one year ago
  7. ganeshie8
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    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

    • one year ago
  8. ganeshie8
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    we can find the side of inner-square

    • one year ago
  9. BIGDOG96
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    Oh

    • one year ago
  10. ganeshie8
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    its (a-b) next, area of square (a-b)^2 next.. ?

    • one year ago
  11. BIGDOG96
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    Not sure.

    • one year ago
  12. ganeshie8
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    second statement would be length of square, right ?

    • one year ago
  13. BIGDOG96
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    Length?

    • one year ago
  14. BIGDOG96
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    You beat me...

    • one year ago
  15. ganeshie8
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    lol, see the diagram, we can find length of side of square, by subtracting b from a length = (a-b)

    • one year ago
  16. ganeshie8
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    so, (2) is the correct one in the sequence

    • one year ago
  17. BIGDOG96
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    Yep

    • one year ago
  18. ganeshie8
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    once we knw length of side of a square, cant we find its area ?

    • one year ago
  19. BIGDOG96
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    Yes so then 1?

    • one year ago
  20. ganeshie8
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    |dw:1347544885906:dw|

    • one year ago
  21. ganeshie8
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    yes

    • one year ago
  22. BIGDOG96
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    4, 2, 1, 3?

    • one year ago
  23. ganeshie8
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    Correct !

    • one year ago
  24. BIGDOG96
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    Thanks

    • one year ago
  25. ganeshie8
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    yw! :)

    • one year ago
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