geometry

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Prove that a triangle with sides : x^2-1, 2x, and x^2 +1 is a right triangle. i substituted the "x"s with 2 and got 5, 4, and 3 and i said that because of the common pythagorean triplets this triangle is a right trianlg is there another way to prove this is a right triangle

  • geometry -

    You have shown it for a specific case, but that does not prove it in general.
    Why don't we just do it
    It appears that x^2 + 1 is the largest side, then
    is (x^2 - 1)^2 + (2x)^2 = (x^2 + 1)^2 ????

    Left side
    = x^4 - 2x^2 + 1 + 4x^2
    = x^4 + 2x^2 + 1

    Right side
    = x^4 + 2x^2 + 1 = Left Side

    done!

  • geometry -

    thanks now it makes so much more sense! :)

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