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BIGDOG96

  • 2 years ago

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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  1. BIGDOG96
    • 2 years ago
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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)

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

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

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

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

  6. BIGDOG96
    • 2 years ago
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    lol will do

  7. ganeshie8
    • 2 years ago
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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

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

  9. BIGDOG96
    • 2 years ago
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    Oh

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

  11. BIGDOG96
    • 2 years ago
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    Not sure.

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

  13. BIGDOG96
    • 2 years ago
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    Length?

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

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

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

  17. BIGDOG96
    • 2 years ago
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    Yep

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

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

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

  21. ganeshie8
    • 2 years ago
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    yes

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

  23. ganeshie8
    • 2 years ago
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    Correct !

  24. BIGDOG96
    • 2 years ago
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    Thanks

  25. ganeshie8
    • 2 years ago
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    yw! :)

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