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Gabylovesyou

  • 2 years ago

Write an indirect proof to show that a rectangle has congruent diagonals. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.

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  1. Gabylovesyou
    • 2 years ago
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    @ganeshie8 @phi @AccessDenied

  2. phi
    • 2 years ago
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    Here is what an indirect proof means http://regentsprep.org/Regents/math/geometry/GP3b/indirectlesson.htm

  3. Gabylovesyou
    • 2 years ago
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    ok.. so i would first start with A rectangle doesn't have congruent diagonals

  4. phi
    • 2 years ago
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    yes. That is as far as I got so far.

  5. Gabylovesyou
    • 2 years ago
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    lol! what happens next ? ;s

  6. phi
    • 2 years ago
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    draw a picture of a rectangle, label the sides , show the right angles. draw in a diagonal

  7. Gabylovesyou
    • 2 years ago
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    |dw:1396376755171:dw|

  8. phi
    • 2 years ago
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    show the angles are all 90º

  9. Gabylovesyou
    • 2 years ago
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    |dw:1396376914251:dw|

  10. phi
    • 2 years ago
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    the first thing that comes to mind is using pythagoras to find the length of a diagonal that leads to a direct proof. maybe we can tweak it to make in indirect.

  11. Gabylovesyou
    • 2 years ago
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    ok

  12. phi
    • 2 years ago
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    |dw:1396377047759:dw|

  13. phi
    • 2 years ago
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    does that make sense (so far ?)

  14. Gabylovesyou
    • 2 years ago
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    yes

  15. phi
    • 2 years ago
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    we could do the same thing for the other diagonal |dw:1396377220075:dw|

  16. phi
    • 2 years ago
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    if the diagonals are not equal to each other, that means a^2+b^2 ≠ a^2 + b^2 and that would only happen if we were not allowed to use the pythagorean theorem. But we have a right triangle (with 90º angle) so we are allowed. therefore our assumption that the diagonals are different must be wrong. that sure sounds convoluted, but it's the best I can come up with.

  17. Gabylovesyou
    • 2 years ago
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    the equal sign thing means does not equal ?

  18. phi
    • 2 years ago
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    yes, ≠ means does not equal

  19. Gabylovesyou
    • 2 years ago
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    ok so i tried doing it in my own words... im going to put it and then delete it

  20. Gabylovesyou
    • 2 years ago
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    @phi

  21. Gabylovesyou
    • 2 years ago
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    @phi DONT LEAVE ME haha

  22. phi
    • 2 years ago
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    I would change that means that a^2 + b^2 does not equal a^2 + b^2 if we are not allowed to that means that a^2 + b^2 does not equal a^2 + b^2 SO we are not allowed

  23. Gabylovesyou
    • 2 years ago
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    thanks

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