Derive Pythagorean Theorem

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

1. nycmathguy

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Derive the Pythagorean Theorem.
Show steps along the way.

Thanks

nycmathguy, Jul 29, 2021
2. 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

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This theorem applies only to right triangles. Yes?

nycmathguy, Jul 29, 2021
4. MathLover1

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Yes

MathLover1, Jul 29, 2021
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