Derive Pythagorean Theorem

Derive the Pythagorean Theorem.
Show steps along the way.

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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

 

This theorem applies only to right triangles. Yes?

 

Yes

 

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