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BIGDOG96 Group Title

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

  • 2 years ago
  • 2 years ago

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  1. BIGDOG96 Group Title
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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)

    • 2 years ago
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  2. ganeshie8 Group Title
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    it CANNOT start with (4)

    • 2 years ago
  3. ganeshie8 Group Title
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    makes no sense to me , check ur options once

    • 2 years ago
  4. BIGDOG96 Group Title
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    That's all the choices I have

    • 2 years ago
  5. ganeshie8 Group Title
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    oops- pls disregard... it does start with (4)

    • 2 years ago
  6. BIGDOG96 Group Title
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    lol will do

    • 2 years ago
  7. ganeshie8 Group Title
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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

    • 2 years ago
  8. ganeshie8 Group Title
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    we can find the side of inner-square

    • 2 years ago
  9. BIGDOG96 Group Title
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    Oh

    • 2 years ago
  10. ganeshie8 Group Title
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    its (a-b) next, area of square (a-b)^2 next.. ?

    • 2 years ago
  11. BIGDOG96 Group Title
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    Not sure.

    • 2 years ago
  12. ganeshie8 Group Title
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    second statement would be length of square, right ?

    • 2 years ago
  13. BIGDOG96 Group Title
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    Length?

    • 2 years ago
  14. BIGDOG96 Group Title
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    You beat me...

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

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

    • 2 years ago
  17. BIGDOG96 Group Title
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    Yep

    • 2 years ago
  18. ganeshie8 Group Title
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    once we knw length of side of a square, cant we find its area ?

    • 2 years ago
  19. BIGDOG96 Group Title
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    Yes so then 1?

    • 2 years ago
  20. ganeshie8 Group Title
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    |dw:1347544885906:dw|

    • 2 years ago
  21. ganeshie8 Group Title
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    yes

    • 2 years ago
  22. BIGDOG96 Group Title
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    4, 2, 1, 3?

    • 2 years ago
  23. ganeshie8 Group Title
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    Correct !

    • 2 years ago
  24. BIGDOG96 Group Title
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    Thanks

    • 2 years ago
  25. ganeshie8 Group Title
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    yw! :)

    • 2 years ago
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