Derive Pythagorean Theorem

Discussion in 'Algebra' started by nycmathguy, Jul 29, 2021.

  1. nycmathguy

    nycmathguy

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    Derive the Pythagorean Theorem.
    Show steps along the way.

    Thanks
     
    nycmathguy, Jul 29, 2021
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  2. nycmathguy

    MathLover1

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    Pythagorean Theorem
    In any right triangle, the sum of the square of the two perpendicular sides is equal to the square of the longest side. For a right triangle with legs measures a and b and length of hypotenuse c, the theorem can be expressed in the form:

    c^2=a^2+b^2

    see attached:


    Area of the large square = Area of four triangles + Area of small square
    A[total]=A[four-triangles]+A[small square]
    (a+b)^2=4((1/2)ab)+c^2
    a^2+2ab+b^2=2ab+c^2
    a^2+b^2=c^2
     

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    MathLover1, Jul 29, 2021
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  3. nycmathguy

    nycmathguy

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    This theorem applies only to right triangles. Yes?
     
    nycmathguy, Jul 29, 2021
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  4. nycmathguy

    MathLover1

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    Yes
     
    MathLover1, Jul 29, 2021
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  5. nycmathguy

    nycmathguy

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    In trigonometry, we'll discuss triangles that are not right triangles. Trigonometry is still many chapters away in the Ron Larson textbook.
     
    nycmathguy, Jul 29, 2021
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